Q25. Use matrices聽A, B, C聽and D聽to... [FREE SOLUTION]

Chapter 4: Q25. (page 164)

Use matrices $A$ , $B$ , $C$ and $D$ to find the following.
$A = [\begin{matrix} 5 & 7 \\ 鈭� 1 & 6 \\ 3 & 鈭� 9 \end{matrix}], 鈥夆赌� B = [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}], 鈥夆赌� C = [\begin{matrix} 0 & 4 \\ 鈭� 2 & 5 \\ 7 & 鈭� 1 \end{matrix}], 鈥夆赌� D = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ 鈭� 3 & 0 \end{matrix}]$
25. $D - B$

Short Answer

Expert verified

The final matrix after performing the indicated matrix operations is $D 鈭� B = [\begin{matrix} 鈭� 2 & 鈭� 1 \\ 4 & 鈭� 1 \\ 鈭� 7 & 鈭� 4 \end{matrix}]$ .

Step by step solution

- Substitute the matrices

Substitute $[\begin{matrix} 6 & 2 \\ 9 & 0 \\ 鈭� 3 & 0 \end{matrix}]$ for D and $[\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}]$ for B into $D 鈭� B$ .

$D 鈭� B = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ 鈭� 3 & 0 \end{matrix}] 鈭� [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}]$

- Perform the matrix subtraction

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.

$\begin{matrix} D 鈭� B = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ 鈭� 3 & 0 \end{matrix}] 鈭� [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}] \\ = [\begin{matrix} 6 鈭� 8 & 2 鈭� 3 \\ 9 鈭� 5 & 0 鈭� 1 \\ 鈭� 3 鈭� 4 & 0 鈭� 4 \end{matrix}] \end{matrix}$

- Simplify

Further simplify the matrix.

$\begin{matrix} D 鈭� B = [\begin{matrix} 6 鈭� 8 & 2 鈭� 3 \\ 9 鈭� 5 & 0 鈭� 1 \\ 鈭� 3 鈭� 4 & 0 鈭� 4 \end{matrix}] \\ = [\begin{matrix} 鈭� 2 & 鈭� 1 \\ 4 & 鈭� 1 \\ 鈭� 7 & 鈭� 4 \end{matrix}] \end{matrix}$

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Short Answer

Step by step solution

- Substitute the matrices

- Perform the matrix subtraction

- Simplify

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Use matricesA, B, Cand Dto find the following.A=57鈭�163鈭�9,鈥夆赌�B=835144,鈥夆赌�C=04鈭�257鈭�1,鈥夆赌�D=6290鈭�3025. D-B

Short Answer

Step by step solution

- Substitute the matrices

- Perform the matrix subtraction

- Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Probability and Statistics

Statistics

Geometry

Study anywhere. Anytime. Across all devices.