Q27. Use matrices聽A, B, Cand D聽to f... [FREE SOLUTION]

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Chapter 4: Q27. (page 164)

Use matrices $A$ , $B$ , $C$ and $D$ to find the following.
$A = [\begin{matrix} 5 & 7 \\ 鈭� 1 & 6 \\ 3 & 鈭� 9 \end{matrix}], 鈥夆赌� B = [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}], 鈥夆赌� C = [\begin{matrix} 0 & 4 \\ 鈭� 2 & 5 \\ 7 & 鈭� 1 \end{matrix}], 鈥夆赌� D = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ 鈭� 3 & 0 \end{matrix}]$
27. $6 B - 2 A$

Short Answer

Expert verified

The final matrix after performing the indicated matrix operations is

$6 B 鈭� 2 A = [\begin{matrix} 38 & 4 \\ 32 & 鈭� 6 \\ 18 & 42 \end{matrix}]$ .

Step by step solution

- Substitute the matrix

Substitute $[\begin{matrix} 5 & 7 \\ 鈭� 1 & 6 \\ 3 & 鈭� 9 \end{matrix}]$ for A and $[\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}]$ for B into $6 B - 2 A$ .

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

- Perform the scalar multiplication

Scalar multiplication -The product of a scalar k and an $m 脳 n$ matrix is an $m 脳 n$ matrix in which each element equals k times the corresponding elements of the original matrix.

Multiply each element of the first matrix $[\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}]$ by 6 and multiply each element of the second matrix $[\begin{matrix} 5 & 7 \\ 鈭� 1 & 6 \\ 3 & 鈭� 9 \end{matrix}]$ by 2.

\begin{matrix} 6 B 鈭� 2 A = 6 [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}] 鈭� 2 [\begin{matrix} 5 & 7 \\ 鈭� 1 & 6 \\ 3 & 鈭� 9 \end{matrix}] \\ = [\begin{matrix} 6 (8) & 6 (3) \\ 6 (5) & 6 (1) \\ 6 (4) & 6 (4) \end{matrix}] 鈭� [\begin{matrix} 2 (5) & 2 (7) \\ 2 (鈭� 1) & 2 (6) \\ 2 (3) & 2 (鈭� 9) \end{matrix}] \\ = [\begin{matrix} 48 & 18 \\ 30 & 6 \\ 24 & 24 \end{matrix}] 鈭� [\begin{matrix} 10 & 14 \\ 鈭� 2 & 12 \\ 6 & 鈭� 18 \end{matrix}] \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.

$\begin{matrix} 6 B 鈭� 2 A = [\begin{matrix} 48 & 18 \\ 30 & 6 \\ 24 & 24 \end{matrix}] 鈭� [\begin{matrix} 10 & 14 \\ 鈭� 2 & 12 \\ 6 & 鈭� 18 \end{matrix}] \\ = [\begin{matrix} 48 鈭� 10 & 18 鈭� 14 \\ 30 鈭� (鈭� 2) & 6 鈭� 12 \\ 24 鈭� 6 & 24 鈭� (鈭� 18) \end{matrix}] \\ = [\begin{matrix} 38 & 4 \\ 32 & 鈭� 6 \\ 18 & 42 \end{matrix}] \end{matrix}$

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Short Answer

Step by step solution

- Substitute the matrix

- Perform the scalar multiplication

- Perform the matrix subtraction

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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�3027. 6B-2A

Short Answer

Step by step solution

- Substitute the matrix

- Perform the scalar multiplication

- Perform the matrix subtraction

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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