5

Let A = [6-8 -21 and let B = 18 13Solve the matrix equation for X : 5X = 2A - B55 -320 25 ~10 -15~2...

Question

Let A = [6-8 -21 and let B = 18 13Solve the matrix equation for X : 5X = 2A - B55 -320 25 ~10 -15~2

Let A = [6 -8 -21 and let B = 18 13 Solve the matrix equation for X : 5X = 2A - B 55 -3 20 25 ~10 -15 ~2



Answers

Solve the matrix equation $A X=B$ for $X$ by finding $A^{-1},$ given $A$ and $B$ as follows.
$$
A=\left[\begin{array}{rrr}{2} & {-5} & {7} \\ {4} & {-3} & {2} \\ {15} & {2} & {6}\end{array}\right], \quad B=\left[\begin{array}{r}{-2} \\ {5} \\ {8}\end{array}\right]
$$

This question is asking us to write a Metrix equation from the system of equations. To get metric form, the we need a X is equal to be formula. They're a is coefficient metrics. I'm gonna write it Red and X. It's gonna be variable metrics and B It's gonna be constant metrics. So if you write it down here Hey, it's gonna be a coefficient off its variable, the variable. We'll be a and B, so we can put it an X and A for a coefficient is going to fight negative things. Three and two can right fight. They get a six, three, two variables. We have two variables. They're A and B there. They're equal to constant variable, which is negative. 47 the negative 17.

We are given two matrices a equal toe minus three minus seven tu minus 950 on be equal toe minus five minus one 00 on three minus four. We need to find a matrix X now. Since the order off the matrices A and B is three cross to so explode to have the same order, let's assume the elements off extra B A B C D e f. Such that two x plus five k is equal. Toby. So putting the values on the matrices will get two multiplied with a B C D E f plus five multiplied with minus three minus seven to minus nine 50 is equal to minus five minus 1003 minus four. So solving and simplifying the left hand side, we'll get to weigh Toby no se toady. So e toe f plus minus 15 minus 35 then minus 45 25 0 is equal to minus five minus 1003 minus four. That is so a minus 15 will be minus 35. You see blast in so D minus 45 to E plus 25 on two if will be equal toe minus five minus 1003 and minus four. Now solving, by creating the corresponding elements, will get two. A minus 15 is equal to minus five, which will give us equal to five. Toby minus 35 is equal toe minus one, which will give us be equal to 17. No C Plus 10 is equal to zero, which will give us equal to minus five. Do T minus 45 is equal to zero, which will give us de equal to 45. Divided by two. No e plus 25 is equal to tree, which will give us E equal to minus 11 on U F equal to minus four, which will give us F equal to minus two. So putting all these values will get the matrix X as equal toe 5 17 minus 5 45 divided by two minus 11 on minus two.

So suppose I have two matrices and I want to solve this matrix situation for X. Okay, so it may look a little confusing but all I'm going to do is just treat A and B like variables or like other constance and I'm just going to get solve this equation, give major text by itself. So what would you do first if this is just an equation trying to get X by itself and move over this five A opposite of adding this, attracting whatever due to one side, I got through to the other. This gives me to matrix X. Can I combine be in a? No, they're different variables. Matrix B -5 times matrix a. Then what I do from here Is X completely by itself. No it's multiplied by two. Okay, I need to give that to opposite of multiplying dividing and I'm going to do this to each of these terms. So really, Matrix X is just found 1/2 times matrix B minus 5/2 or plus negative 5/2 times matrix A. So I just have to do a bunch of matrix operations to find this. So first let's find one half times B um so one half times matrix B to multiply a matrix I'm gonna do is multiply each of these terms by one half and solve from there. Okay, so this will be negative five over to anything times 00, 3/2 negative one half zero and negative 4/2 or negative to I'm gonna leave it as a fraction for now. Plus now I want to find negative 5/2 times a day. So I'm gonna multiply each of these By -5/2. Okay, doing this. So negative five or two negative tim's name is positive positive 15 over to This will be negative or positive 10 over to This will be negative 25 over to write five times 7 positive 35. It's going to be negative positive 35/2. Positive 45 over to anything times 00. Okay, so now that I'm multiplied into these matrices, I'm just going to add them together. Since I multiplied by a negative this ends up canceling and this is also negative. She's if that works okay? So add all these together at each of the components together. Negative five or two plus 15 negative five plus 15. 10 positive 10 over to negative one half plus 35. So negative 1, 35 is 34/2, zero plus negative 10 over to and then 45/2 plus zero. Okay, 3/2 minus 25. Negative 22/2. And then negative four over two. And finally, I could just simplify whatever I can. So 10/2 is just five negative five negative 11. 34 divided by two is 17. I'm gonna leave. This is 45/2 and then negative two. And this will be my matrix X. After I performed indicated operations

Given that Matrix A is equal to minus three minus seven to minus nine on 50 on Matrix B is equal to minus five, minus one 00 and three minus four. We need to find the Matrix X now, since and we are matrices off the order three cross toe so the X will also be off the order. Three. Cross to Let's Take the elements as a B, C, D and E f or the Matrix sex such that two weeks plus a equals b. So putting the matrices we'll get to multiplied with a B C D E f plus A, which is minus three minus seven to minus +950 is equal to minus five minus 1003 on minus four. So this will become the way Toby, so c o d two e two f plus minus three minus seven to minus 950 is equal toe minus five minus 1003 minus four. Solving on simplifying, we'll get to a minus tree. You will be minus seven. You'll see my in the stool through the minus nine to E plus five on Do If on the left hand side. This will be equal to minus five, minus 1003 and minus four. So equating the corresponding elements in the matrices, we'll get no way minus tree is equal to minus five, which means no way is equal. Toe eight, which means is equal to four. Next will be minus seven is equal to minus one, which means to a is equal to six, which means is equal to three. Next you'll see minus two is equal to do. That is, do you see is equal. Toto, which will give us sees equal to one no. D minus nine is equal to zero, which means Cody is equal to nine, which will give us de equal to nine. Divided by two no e Bless five is equal to three, which means to ease equal to minus two. That is, evil be equal to minus one on two. F is equal to minus four, which means F is equal to minus two. So therefore, putting the values in the matrix off X. We'll get the matrix as four three one nine, divided by tool minus one on minus


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