5

Adjoin on the right ofthen use row operations t0 find the inverse Aof the given matrix A_Find the inverse. Select the correct choice below and, if necessary; fill i...

Question

Adjoin on the right ofthen use row operations t0 find the inverse Aof the given matrix A_Find the inverse. Select the correct choice below and, if necessary; fill in the answer box to complete your choice.0 A. A -1 The matrix is not invertible

Adjoin on the right of then use row operations t0 find the inverse A of the given matrix A_ Find the inverse. Select the correct choice below and, if necessary; fill in the answer box to complete your choice. 0 A. A -1 The matrix is not invertible



Answers

decide whether the matrix is invertible, and if so, use the adjoint method to find its inverse. $$A=\left[\begin{array}{rrr} 2 & -3 & 5 \\ 0 & 1 & -3 \\ 0 & 0 & 2 \end{array}\right]$$

With a two by two matrix. We can use 1/80 minus B c times D B negative C A. To find the inverse of a matrix of a matrix is a night of a A. Then the inverse matrix would be one over a d, which would be a squared, um, minus a squared or minus Negative a squared times T, which is a opposite B, which is a opposite. See, which is negative A and a witch, is it? Hey, it won over a squared Plus Ace bird is to a squared. Times are matrix here, which would then get distributed So we would have a over to a squared A over to a square negative a over to a squared A over to a squared, which would be equal to, uh, one over to a one over to a negative one over to a on one over to a as all the aces. If I

Number 431. They want us to find the inverse of this four by four matrix here. Okay, left the bracket open. Because the way we're going to do this, we write the identity matrix on the right. Okay, so four by four identity matrix on the right and we want to perform role operations until we get the identity matrix on the left. Okay, so we're gonna work one column at a time. We already have a one in the upper left and all zeros in the first column. Okay, Second column. We want to get a one here and the rest zeros. So since we want a zero right here, I am going to subtract row two from row three and put that in Rose three. Okay, so we're doing Rose three. Mine is wrote to All right, so rewrite the first two rose. No. And each element in row three subtracted from row 20 minus zero is 01 minus 01 minus 101 minus zero is one and so on. Yeah, and just rewrite Row four. All right, So, row, uh, column two is finished as we want it. Okay, Column three. We want one right here, and we want the rest of them zero. So I'm gonna dio row one minus row three and put it in Row one and row four, minus row three and put it in a row for Okay. So I'm killing two birds with one stone here because I want to get a zero right here and a zero right here. And when we subtract these ones from this one that will give us the zeros we need. So each element and row one minus each element in row three and that will give us 1001 and 11 11 negative 10 re copy wrote to re copy Row three and each element in Row four minus each element and row three one minus negative. One is going to give us a to 01 negative one and one. Okay, so our third column is complete Now for the fourth column. We want this value here to be a one, and we want the rest of these to be zero. Okay, so I am going to multiply row for times one half, and that will give us a one right here. Okay. And then I am gonna add half. I'm gonna add that to Row three. So half of our four plus row three. And I'm gonna subtract half of our four from row two. And I'm going to subtract half of our four from row one, minus half of our four. Okay, so when we do, half of our four will get a one here. And then we only added to this one will get a zero when we do, one minus half of two will get 01 minus half of two will get zero. So that's what we want. So pretty easy, operations. But we're doing four rows. All right, so in the first row, first row, let me see. We're doing our one. Okay? 10 All zeros said for the top left, and we're getting one half negative. One half negative. One half, second row. Um, we're getting a zero half. Half negative. One half, Third row, zero negative. One half. If half and forth. Row zero, half negative. One half. Half. Okay. So now we have the identity matrix on the left. See, we have all ones in the main diagonal and old zeros for the rest of the elements. So this this matrix on the right is your inverse matrix. So if the original matrix was a this is how we would write the inverse matrix. Now, in their answer, they factored out a one half. Okay, so let's just do that. So a half times what will give us one? Well, I have times two will give us one. And this is one negative one negative one. This is zero one one negative one. This is zero negative. 11 one. And this 01 negative. One one. Okay, so we factored out a half. So wherever there's a one half, it's just one, because a half times one will give us a half where there's negative one half its negative one and so on. Okay, so this matrix with the one half factored out is our inverse major

What the determined matrix given on the left here is convertible and if it is fine it's in verse eight of the negative. First by the ad joint method. So let's no it's an important definitions. First of all, the inverse of a is equal to buy the ad joint method one over the determinative eight times the joint today where the ad join today is the transpose of a matrix formed by the co factors for each entry and A. And we have to make a note of the fact that A. Is in veritable if it's determined does not equal zero. So first let's find the determinant of a to make sure it can be inverted determinant of A is simply shoot times 93 minutes, zero minus 5,000,003 minutes. Zero plus five to negative four plus two or negative one. This is not equal zero. So we can invert a Let's now find its inverse by the joint method. The co factor matrix for a. I. J. Is given on the left here, and simply taking the transpose gives us the matrix on the right next to find the inverse of A. We simply have to multiply every single one of these entries by one over determining A or one over negative one, which gives inverse A. As is boxed in at the bottom here.

As I asked him were given a matrix and resting Slagle it of this matrix is convertible and if so to use the add joint method Find its inverse. This is the three x 3 matrix a equals 255 other A -1 -10 and 243 shitty faggot. That's me first is finally determined into this matrix A. This is the determinant of this three x 3 matrix. Using co factor expansions will expand across the top row. This is two times the determinant negative 1043 a minus five times the determinant of negative 10 to 3 plus five times the determinant of negative one. Negative 1 to 4. Down this matter this is equal to two times negative three minus zero minus five times negative three minus zero plus five times negative four plus two. Which simplifies to negative six plus 15 minus 10. Which is equal to negative one. Which of course is non zero Since are determined as non zero. It's it follows that our matrix A is in fact in vertebral. I I fear him from this section. Remember told somebody Now to find its inverse first. Let's find co factors of a. So the co factors C11 is the determinant of -1043. Of course, it's not true. Okay. Damn. Which is -3. co fracture. See 1 2. This is the opposite of the determinant of -10 23 Actually his second stuff three. and the cool factor C13. This is the determinant of the matrix negative one. Negative 1 to 4. Right. Right, right. This is negative four minus negative two. Or negative to co factor C 21 This is the opposite The determinant 5543. This is the opposite of 15 -20 or positive five. I'm stuck. The co factor C 22 This is the Derivative after this is the determinant of 2 5-3 lost. And this is negative four is the big guy. Co factors C 23 is the opposite of the determined 2, 5- four. He didn't bad news, which is to the future. I'm sorry mm. Likewise, we find that the co factor C31 is five. Co factors C32 is negative five. And the co factor C 33 is three. My turn. Therefore, with all these co factors, you can form a matrix of co factors. So any woman. Yeah. And so this is the matrix The country's negative 3 3 -2, 5 -4, 2, jewish man And 5 -5. 3. Come on, that's me, 14 year old Adam Friedland. And therefore the ad joint matrix. Perhaps the classical adjunct matrix hard to say with action means at join today. Well this is defined to be the transposed of the matrix of co factors of A. And so you're looking at our matrix of co factors. This is the matrix negative 355 Then I have three negative two, negative four negative 52 And number three like this. Now we know from the theorem at a inverse is equal to one over the determinant of the matrix A Times the ad joined today. Take you to get new since the determinant was negative one. This gives us the matrix centuries of the opposite of the edge. So we have positive three negative five, negative five, negative three, positive four, positive five And positive to -2 -3. And so this is our inverse, a inverse.


Similar Solved Questions

5 answers
One mole of a weak acid HA was dissolved in 1.8 L of solution_ After the system had come to equilibrium; the concentration of HA was found to be 0.43 M. Calculate Ka for HA:KaSubmit AnswerTry Another Versionitem attempts remaining
One mole of a weak acid HA was dissolved in 1.8 L of solution_ After the system had come to equilibrium; the concentration of HA was found to be 0.43 M. Calculate Ka for HA: Ka Submit Answer Try Another Version item attempts remaining...
5 answers
Convert from rectangular to cylindrical coordinates_ (3, -3, 9)(r, 0,2) =
Convert from rectangular to cylindrical coordinates_ (3, -3, 9) (r, 0,2) =...
5 answers
Prove Or give counterexample: If V1, U2, Uk IS linearly independent list of vectors in V and C1, Ck € F with C # 0 for all thenC1UI . C2U2 .CkUkis linearly independent_
Prove Or give counterexample: If V1, U2, Uk IS linearly independent list of vectors in V and C1, Ck € F with C # 0 for all then C1UI . C2U2 . CkUk is linearly independent_...
5 answers
7. Write the equilibrium constant K for the following reaction: a) C3H8(g) 502(g) + 3C02(g) 4H2O()
7. Write the equilibrium constant K for the following reaction: a) C3H8(g) 502(g) + 3C02(g) 4H2O()...
5 answers
1). Compare the heat loss between a standard double pane window 0.9 m by 0.47 m hat has a gap filled with air that is 3 mm wide with a triple pane windows of the same size that has two gaps with air inside them, each 3 mm wide: The outside temperature is 88 C and the inside temperature is 259 C* for both situations The glass between the two gaps is 4 mm wide.
1). Compare the heat loss between a standard double pane window 0.9 m by 0.47 m hat has a gap filled with air that is 3 mm wide with a triple pane windows of the same size that has two gaps with air inside them, each 3 mm wide: The outside temperature is 88 C and the inside temperature is 259 C* for...
5 answers
In Fig. $15-31$, two identical springs of spring constant $7580 mathrm{~N} / mathrm{m}$are attached to a block of mass $0.245 mathrm{~kg}$. What is the frequency of oscillation on the frictionless floor?
In Fig. $15-31$, two identical springs of spring constant $7580 mathrm{~N} / mathrm{m}$ are attached to a block of mass $0.245 mathrm{~kg}$. What is the frequency of oscillation on the frictionless floor?...
5 answers
Convert between names and structures of carboxylic acidQuestionHow many carbons are there in the main chain of the compound 2-hydroxy-3-methylbutanoic acid?Your answer should be an integer (a whole number):Provide your answer below:carbonsMORE INSTRUCTIONSUBMITContent attribution
Convert between names and structures of carboxylic acid Question How many carbons are there in the main chain of the compound 2-hydroxy-3-methylbutanoic acid? Your answer should be an integer (a whole number): Provide your answer below: carbons MORE INSTRUCTION SUBMIT Content attribution...
5 answers
Find the area of the region bounded by the graphs ot the equations whole number:Round your njawert0 the mared
Find the area of the region bounded by the graphs ot the equations whole number: Round your njawert0 the mared...
5 answers
If a person in a crowd does not help in an apparent emergency situation because many other people are present, that person is falling victim to the phenomenon of ____________ __________ ______________.
If a person in a crowd does not help in an apparent emergency situation because many other people are present, that person is falling victim to the phenomenon of ____________ __________ ______________....
1 answers
For different positive values of $k,$ determine how many times $y=\sin k x$ intersects $y=x .$ In particular, what is the largest value of $k$ for which there is only one intersection? Try to determine the largest value of $k$ for which there are three intersections.
For different positive values of $k,$ determine how many times $y=\sin k x$ intersects $y=x .$ In particular, what is the largest value of $k$ for which there is only one intersection? Try to determine the largest value of $k$ for which there are three intersections....
5 answers
What should be the next steps in the identification of yourunknown (Hint: use your knowledge of the 5 I's!)?
What should be the next steps in the identification of your unknown (Hint: use your knowledge of the 5 I's!)?...
5 answers
The lifetimes of group of 10 light bulbs are given below: 221,645,538,941,269,893,703,536,823 651. The standard deviation of the lifetimes is (to two decimal places)Select one: 622.0058155.11386884.00241.15
The lifetimes of group of 10 light bulbs are given below: 221,645,538,941,269,893,703,536,823 651. The standard deviation of the lifetimes is (to two decimal places) Select one: 622.00 58155.11 386884.00 241.15...
5 answers
QurcomtiarJus Econ 5.6.17 Guur tlanntetutraru {40 ucuMcrh Hot nuta Gah Vennede ecenanktoth 6* compoududLeuta @luacnHr4n} mJicatnMeee eamandeutr Mad
Qurcomtiar Jus Econ 5.6.17 Guur tlanntetutraru {40 ucu Mcrh Hot nuta Gah Vennede ecenan ktoth 6* compoudud Le uta @luacn Hr4n} m Jicatn Meee eamandeutr Mad...
1 answers
"Use MATLAB as required by the problem statement Limit yourself to 5 iteration by hand for all problems (fewer iterations are allowable as long as you meet the conditions set forth by the problem):
"Use MATLAB as required by the problem statement Limit yourself to 5 iteration by hand for all problems (fewer iterations are allowable as long as you meet the conditions set forth by the problem):...
5 answers
[0/2 Points]DETAILSPREVIOUS ANSWERSSCALCET8 6.5.014.Find the numbers such that the average value 0f ((x)1Ox 6x? on the Interval [0, b] Is equal to(staller value)(larger value)
[0/2 Points] DETAILS PREVIOUS ANSWERS SCALCET8 6.5.014. Find the numbers such that the average value 0f ((x) 1Ox 6x? on the Interval [0, b] Is equal to (staller value) (larger value)...
5 answers
Find the equilibrium constant Kc for the reaction: A + 2 B=D-E Givcn: A - 2B=C (Kc)l = 12C=D-E(Kc) =1.80.62.161.5Determine Kp for the reaction: 2 NCI3 (g) N2 (g) + 3 C12 (g), given that the equilibrium pressures are: P(NCI3) = 0.16 atm; P(N2) = 2.31atm; P(CI2) = 0.0565 atm_7.750.01631.220.816
Find the equilibrium constant Kc for the reaction: A + 2 B=D-E Givcn: A - 2B=C (Kc)l = 12 C=D-E (Kc) =1.8 0.6 2.16 1.5 Determine Kp for the reaction: 2 NCI3 (g) N2 (g) + 3 C12 (g), given that the equilibrium pressures are: P(NCI3) = 0.16 atm; P(N2) = 2.31atm; P(CI2) = 0.0565 atm_ 7.75 0.0163 1.22 0....

-- 0.022558--