First slide

Operations of matrix

Question

If $[\begin{array}{cc} i & 0 \\ 3 & - i \end{array}] + X = [\begin{array}{cc} i & 2 \\ 3 & 4 + i \end{array}] - X$ then X is equal to

Moderate

A

$[\begin{array}{cc} 0 & - 1 \\ 3 & i \end{array}]$
B

$[\begin{array}{cc} 0 & 1 \\ 0 & 2 + i \end{array}]$
C

$[\begin{array}{cc} 1 & 0 \\ 0 & 2 - i \end{array}]$
D

$[\begin{array}{cc} i & 2 \\ 0 & 2 + i \end{array}]$

Solution

$\begin{array}{l} 2 X = [\begin{array}{cc} i & 2 \\ 3 & 4 + i \end{array}] - [\begin{array}{cc} i & 0 \\ 3 & - i \end{array}] = [\begin{array}{lc} 0 & 2 \\ 0 & 4 + 2 i \end{array}] \\ \Rightarrow X = [\begin{array}{cc} 0 & 1 \\ 0 & 2 + i \end{array}] \end{array}$

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