Chapter 4: Q42. (page 166)

Which matrix equals $[\begin{matrix} 5 & - 2 \\ - 3 & 7 \end{matrix}] - [\begin{matrix} 3 & 4 \\ - 5 & 6 \end{matrix}]$ ?
A. $[\begin{matrix} 2 & 2 \\ - 8 & 1 \end{matrix}]$ B. $[\begin{matrix} 8 & - 6 \\ - 8 & 1 \end{matrix}]$ C. $[\begin{matrix} 2 & 2 \\ 2 & 1 \end{matrix}]$ D. $[\begin{matrix} 2 & - 6 \\ 2 & 1 \end{matrix}]$

Short Answer

Expert verified

The final matrix after performing the indicated matrix operation is

$[\begin{matrix} 5 & - 2 \\ - 3 & 7 \end{matrix}] - [\begin{matrix} 3 & 4 \\ - 5 & 6 \end{matrix}] = [\begin{matrix} 2 & - 6 \\ 2 & 1 \end{matrix}]$ , which is option D.

Step by step solution

- Define concept of matrix subtraction

If A and B are two matrices of order $m \times n$ , then the subtraction of the two matrices will also yield a matrix of order $m \times n$ wherein each element is the difference of the corresponding elements.

- Subtract corresponding elements

In order to find $[\begin{matrix} 5 & - 2 \\ - 3 & 7 \end{matrix}] - [\begin{matrix} 3 & 4 \\ - 5 & 6 \end{matrix}]$ , add corresponding elements of both the matrices.

$[\begin{matrix} 5 & - 2 \\ - 3 & 7 \end{matrix}] - [\begin{matrix} 3 & 4 \\ - 5 & 6 \end{matrix}] = [\begin{matrix} 5 - 3 & - 2 - 4 \\ - 3 - (- 5) & 7 - 6 \end{matrix}]$

- Simplify the matrix

Further simplify the matrix by subtracting the elements.

$\begin{matrix} [\begin{matrix} 5 & - 2 \\ - 3 & 7 \end{matrix}] - [\begin{matrix} 3 & 4 \\ - 5 & 6 \end{matrix}] = [\begin{matrix} 5 - 3 & - 2 - 4 \\ - 3 - (- 5) & 7 - 6 \end{matrix}] \\ = [\begin{matrix} 2 & - 6 \\ 2 & 1 \end{matrix}] \end{matrix}$

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Short Answer

Step by step solution

- Define concept of matrix subtraction

- Subtract corresponding elements

- Simplify the matrix

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Which matrix equals5−2−37−34−56?A. 22−81 B.8−6−81C.2221 D.2−621

Short Answer

Step by step solution

- Define concept of matrix subtraction

- Subtract corresponding elements

- Simplify the matrix

One App. One Place for Learning.

Most popular questions from this chapter

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