Find the additive inverse of following matrices.

Question

Question:

Find the additive inverse of following matrices.

A =$~\left[ \begin{matrix} 2 & 4 \ -2 & 1 \ \end{matrix} ight]$	B =$~\left[ \begin{matrix} 1 & 0 & -1 \ 2 & -1 & 3 \ 3 & -2 & 1 \ \end{matrix} ight]$
C = $\left[ \begin{matrix} 4 \ -2 \ \end{matrix} ight]$	D =$~\left[ \begin{matrix} 1 & 0 \ -3 & -2 \ 2 & 1 \ \end{matrix} ight]$
E = $\left[ \begin{matrix} 1 & 0 \ 0 & 1 \ \end{matrix} ight]$	F = $\left[ \begin{matrix} \sqrt{3} & 1 \ -1 & \sqrt{2} \ \end{matrix} ight]$

Accepted Answer

Solution:

The additive inverse of a matrix is obtained by changing the sign of each entry. So, according to the definition:

(i) Additive inverse of A = $-$A = $\left[ \begin{matrix} -2 & -4 \ 2 & -1 \ \end{matrix} ight]$

(ii) Additive inverse of B = $-$B = $\left[ \begin{matrix} -1 & 0 & 1 \ -2 & 1 & -3 \ -3 & 2 & -1 \ \end{matrix} ight]$

(iii) Additive inverse of C = $-$C = $\left[ \begin{matrix} -4 \ 2 \ \end{matrix} ight]$

(iv) Additive inverse of D = $-$D = $\left[ \begin{matrix} -1 & 0 \ 3 & 2 \ -2 & -1 \ \end{matrix} ight]$

(v) Additive inverse of E = $-$E = $\left[ \begin{matrix} -1 & 0 \ 0 & -1 \ \end{matrix} ight]$

(vi) Additive inverse of F = $-$F = $\left[ \begin{matrix} -\sqrt{3} & -1 \ 1 & -\sqrt{2} \ \end{matrix} ight]$

A =$~\left[ \begin{matrix} 2 & 4 \\ -2 & 1 \\ \end{matrix} \right]$	B =$~\left[ \begin{matrix} 1 & 0 & -1 \\ 2 & -1 & 3 \\ 3 & -2 & 1 \\ \end{matrix} \right]$
C = $\left[ \begin{matrix} 4 \\ -2 \\ \end{matrix} \right]$	D =$~\left[ \begin{matrix} 1 & 0 \\ -3 & -2 \\ 2 & 1 \\ \end{matrix} \right]$
E = $\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]$	F = $\left[ \begin{matrix} \sqrt{3} & 1 \\ -1 & \sqrt{2} \\ \end{matrix} \right]$