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Adjoin on the right of A, then use row operations to find the inverse Aof the given matrix A.Find the inverse. Select the correct choice below and, if necessary, fi...

Question

Adjoin on the right of A, then use row operations to 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 choiceOA. A `The matrix is not invertible.

Adjoin on the right of A, then use row operations to 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 OA. A ` The matrix is not invertible.



Answers

decide whether the matrix is invertible, and if so, use the adjoint method to find its inverse. $$A=\left[\begin{array}{llll} 1 & 3 & 1 & 1 \\ 2 & 5 & 2 & 2 \\ 1 & 3 & 8 & 9 \\ 1 & 3 & 2 & 2 \end{array}\right]$$

Why we want to determine if matrix A given on the left here is inevitable and if it is, we want to find its inverse matrix. Using the add joint method, let's make note of a couple important definitions to solve this problem first, the inverse of A is equal to one over the determinative eight times the ad joined today with the advent of A. Is the transpose of a matrix formed by all the co factors of A. And A. Is inevitable. If and only if the determinant does not equal zero given our matrix A. On the left. As I've already noted, let's start by finding the determinant to make sure it's investable. Using a three by three determinant formula. We have determined A equals two times two minus zero minus negative 3. 10 0 minus zero plus 5. 10 0 minus zero or simply for since this is not equal zero, we can invert A and we proceed to finding the inverse. So first let's find the AD joint. To start off, let's find the CO factor matrix given on the left. Then by simply taking the transpose, we get co factor transposed shown on the right. Finally, to solve for inverse A. We divide every entry in the transposed co factor matrix by four are determinant, dividing by one over Providing by four gives us our final solution inverse a list at the bottom of this document.

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

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.


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