Question

01. Two matrixes A and B are given. Express B^-1 through x and A.

❌ Don't spamming

✅ Quality answer needed. ​

Answer 1

Answer:

Matrix addition. If A and B are matrices of the same size, then they can be added. (This is similar to the restriction on adding vectors, namely, only vectors from the same space R n can be added; you cannot add a 2‐vector to a 3‐vector, for example.) If A = [aij] and B = [bij] are both m x n matrices, then their sum, C = A + B, is also an m x n matrix, and its entries are given by the formula

Step-by-step explanation:

give thanks to me

Answer 2

Step-by-step explanation:

Given:

$A=\left[\begin{array}{ccc}3x&-4x&2x\\-2x&x&0\\-x&-x&x\end{array}\right]$

$B=\left[\begin{array}{ccc}x&2x&-2x\\2x&5x&-4x\\3x&7x&-5x\end{array}\right]$

To find:

Express $B^{-1}$ through x and A.

Solution:

Step 1: Take x common from A,so that to simplify the process

$A=x\left[\begin{array}{ccc}3&-4&2\\-2&1&0\\-1&-1&1\end{array}\right]$

$B=x\left[\begin{array}{ccc}1&2&-2\\2&5&-4\\3&7&-5\end{array}\right]$

Step 2: Multiply A and B

$AB=x\left[\begin{array}{ccc}3&-4&2\\-2&1&0\\-1&-1&1\end{array}\right]x\left[\begin{array}{ccc}1&2&-2\\2&5&-4\\3&7&-5\end{array}\right]$

thus

$AB=x^2\left[\begin{array}{ccc}3&-4&2\\-2&1&0\\-1&-1&1\end{array}\right]\left[\begin{array}{ccc}1&2&-2\\2&5&-4\\3&7&-5\end{array}\right]$

$AB=x^2\left[\begin{array}{ccc}3(1)+(-4)(2)+2(3)&3(2)+(-4)(5)+2(7)&3(-2)+(-4)(-4)+2(-5)\\ (-2)(1)+1(2)+0(3)&(-2)(2)+1(5)+0(7)&(-2)(-2)+(1)(-4)+0(-5)\\(-1)(1)+(-1)(2)+1(3)&(-1)(2)+(-1)(5)+1(7)&(-1)(-2)+(-1)(-4)+1(-5)\end{array}\right]$

on solving,one will get an identity matrix

$AB=x^2\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

Step 3: Find B inverse

$AB=x^2I$

$A=x^2B^{-1}$

$B^{-1}=\frac{A}{x^2}$

or

$B^{-1}=Ax^{-2}$

Final answer:

$\boxed{\bold{B^{-1}=\frac{A}{x^2}=Ax^{-2}}}$

Hope it helps you.

To learn more on brainly:

x+ y + z=3

2x-y+z=2

x-2y+ 32 = 2

Solve the following system of eqs

https://brainly.in/question/41229936

solve 5X-Y+4Z=5,2x+3y+5z=2,7x-2y+6z=5 by cramer's rule differentiate tha following with respect x

https://brainly.in/question/31174645