Find a matrix X such that 2A + B + X = 0 , where \(A=\begin{bmatrix} -1 & 2 \\\ 3 & 4 \end{bmatrix} \ \text{and} \;\rm B =\ \begin{bmatrix} 3 & -2 \\\ 1 & 5 \end{bmatrix} \ ?\)
Concept:
Two matrices may be added or subtracted only if they have the same dimension; that is, they must have the same number of rows and columns.
Addition or subtraction is accomplished by adding or subtracting corresponding elements.
Calculations:
Given, \(A=\begin{bmatrix} -1 & 2 \\ 3 & 4 \end{bmatrix} \ \text{and} \; \rm B = \ \begin{bmatrix} 3 & -2 \\ 1 & 5 \end{bmatrix} \)
Consider, 2A + B + X = 0
⇒ \( \rm 2\begin{bmatrix} -1 & 2 \\ 3 & 4 \end{bmatrix} + \ \begin{bmatrix} 3 & -2 \\ 1 & 5 \end{bmatrix} + X = \begin{bmatrix} 0 & 0\\ 0 &0 \end{bmatrix}\)
Two matrices may be added or subtracted only if they have the same dimension; that is, they must have the same number of rows and columns. Addition or subtraction is accomplished by adding or subtracting corresponding elements.
⇒ \( \rm \begin{bmatrix} 1 & 2 \\ 7 & 13 \end{bmatrix} + X = \begin{bmatrix} 0 & 0\\ 0 & 0 \end{bmatrix}\)
⇒ X = \( \begin{bmatrix} 0 & 0\\ 0 &0 \end{bmatrix} \) - \( \rm \begin{bmatrix} 1 & 2 \\ 7 & 13 \end{bmatrix} \)
⇒ X = \( \rm \begin{bmatrix} -1 & -2 \\ - 7 & -13 \end{bmatrix} \)
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