Question

If A =[ 1 -1
2 3]
and C = [ 2 3
1 -11]
find matrix B such that BA = C​

Answer 1

Let the order of the matrix X be a × b Comparing the two matrices, we get, 2x + y = 3 … (1) x + 3y = − 11 … (2) Multiplying (1) with 3, we get, 6x + 3y = 9 … (3) Subtracting (2) from (3), we get, 5x = 20 x = 4 From (1), we have: y = 3 − 2x = 3 − 8 = −5 x = [(4), (-5)]Read more on Sarthaks.com - https://www.sarthaks.com/151135/if-a-2-1-1-3-and-b-3-11-find-the-matrix-x-such-that-ax-b

Answer 2

Step-by-step explanation:

Given:

$A=\left[\begin{array}{cc}1&-1\\2&3\end{array}\right]$

$C=\left[\begin{array}{cc}2&3\\1&-11\end{array}\right]$

To find:find matrix B such that BA = C

Solution:

Step 1: Multiply with A-1 both sides

$BAA^{-1}=CA^{-1}$

$B=CA^{-1}$

Step 2: Find A-1

|A|=3+2=5

$A^{-1}=\frac{Adj(A)}{|A|}$

$Adj(A)=\left[\begin{array}{cc}3&1\\-2&1\end{array}\right]$

$A^{-1}=\frac{1}{5}\left[\begin{array}{cc}3&1\\-2&1\end{array}\right]$

Step 3: Multiply C and A-1

$B=\frac{1}{5}\left[\begin{array}{cc}2&3\\1&-11\end{array}\right]\times\left[\begin{array}{cc}3&1\\-2&1\end{array}\right]$

$B=\frac{1}{5}\left[\begin{array}{cc}6-6&2+3\\3+22&1-11\end{array}\right]$

$B=\frac{1}{5}\left[\begin{array}{cc}0&5\\25&-10\end{array}\right]$

$B=\left[\begin{array}{cc}\frac{0}{5}&\frac{5}{5}\\\\\frac{25}{5}&-\frac{10}{5}\end{array}\right]$

Final answer:

$B=\left[\begin{array}{cc}0&1\\5&-2\end{array}\right]$

Hope it helps you.

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