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0 votes
1.3k views
in Linear Equations by (49.9k points)
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If A \( \begin{pmatrix} 3&2 \\ 1 &-1 \end{pmatrix}\) = \( \begin{pmatrix} 4&1 \\ 2 &3 \end{pmatrix}\)then a = ?

A .\( \begin{pmatrix} 1&-1\\ 1 &1 \end{pmatrix}\)

B. \( \begin{pmatrix} 1&1 \\ -1 &1 \end{pmatrix}\)

C.\( \begin{pmatrix} 1&1 \\ 1 &-1 \end{pmatrix}\)

D. none of these

1 Answer

+1 vote
by (55.0k points)
selected by
 
Best answer

The matrix on the R.H.S of the given matrix is of order 2 x 2 and the one given on left side is 2 x 2 . Therefore A has to be a 2 x 2 matrix.

Let A = 

3a+b = 4 ----- 1 

2a-b = 1 ------ 2 

3c+d= 2 ------ 3 

2c-d=3 ------- 4 

Using 1 and 2 

a =1 

b =1 

Using 3 and 4 

c =1 

d = -1 

So A becomes \( \begin{pmatrix} 1&1 \\ 1 &-1 \end{pmatrix}\)

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