Chapter 4: Q42. (page 166)

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

Short Answer

Expert verified

The final matrix after performing the indicated matrix operation is

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

Step by step solution

- Define concept of matrix subtraction

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

- Subtract corresponding elements

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

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

- Simplify the matrix

Further simplify the matrix by subtracting the elements.

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

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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鈭�2鈭�37鈭�34鈭�56?A. 22鈭�81 B.8鈭�6鈭�81C.2221 D.2鈭�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

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Logic and Functions

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.