​ If ((3,-2),(5,6)) + 2A =((5,6),(-7,10)) then A = ? ​

Question

If \(​​​​\begin{pmatrix} 3 & -2 \\ 5 & 6 \\ \end{pmatrix}\) + 2A = \(​​​​\begin{pmatrix} 5 & 6 \\ -7 & 10 \\ \end{pmatrix}\) then A = ?

A. \(​​​​\begin{pmatrix} 1 & 3 \\ -5 & 4 \\ \end{pmatrix}\)

B. \(​​​​\begin{pmatrix} -1 & 5 \\ -3 & 4 \\ \end{pmatrix}\)

C. \(​​​​\begin{pmatrix} 1 & 4 \\ -6 & 2 \\ \end{pmatrix}\)

D. none of these

Answer 1

Correct answer is\(​​​​\begin{pmatrix} 3 & -2 \\ 5 & 6 \\ \end{pmatrix}\)

\(​​​​\begin{pmatrix} 3 & -2 \\ 5 & 6 \\ \end{pmatrix}\) + 2A = \(​​​​\begin{pmatrix} 5 & 6 \\ -7 & 10 \\ \end{pmatrix}\)

⇒ 2A = \(​​​​\begin{pmatrix} 5 & 6 \\ -7 & 10 \\ \end{pmatrix}\) - \(​​​​\begin{pmatrix} 3 & -2 \\ 5 & 6 \\ \end{pmatrix}\)

⇒ 2A = \(​​​​\begin{pmatrix} 2 & 8 \\ -12 & 4 \\ \end{pmatrix}\)

Dividing the matrix by 2 

A = \(​​​​\begin{pmatrix} 1 & 4 \\ -6 & 2 \\ \end{pmatrix}\)