Chapter 4: Q8. (page 164)

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

Short Answer

Expert verified

The final matrix after performing the indicated matrix operations is

$A + B + C = [\begin{matrix} 10 & 6 \\ - 1 & 15 \end{matrix}]$

Step by step solution

- Substitute the matrices

Substitute $[\begin{matrix} 2 & 3 \\ 5 & 6 \end{matrix}]$ for A, $[\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}]$ for B and $[\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}]$ for C into $A + B + C$

$A + B + C = [\begin{matrix} 2 & 3 \\ 5 & 6 \end{matrix}] + [\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}] + [\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}]$

- Perform the matrix addition

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

$\begin{array}{l} A + B + C = [\begin{matrix} 2 & 3 \\ 5 & 6 \end{matrix}] + [\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}] + [\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}] \\ = [\begin{matrix} 2 - 1 + 9 & 3 + 7 - 4 \\ 5 + 0 - 6 & 6 + 4 + 5 \end{matrix}] \end{array}$

- Simplify

Further simplify the matrix.

$\begin{array}{l} A + B + C = [\begin{matrix} 2 - 1 + 9 & 3 + 7 - 4 \\ 5 + 0 - 6 & 6 + 4 + 5 \end{matrix}] \\ = [\begin{matrix} 10 & 6 \\ - 1 & 15 \end{matrix}] \end{array}$

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

Short Answer

Step by step solution

- Substitute the matrices

- Perform the matrix addition

- Simplify

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Use matrices A, B, and C to find the following.A=2356,B=−1704,C=9−4−65A+B+C

Short Answer

Step by step solution

- Substitute the matrices

- Perform the matrix addition

- Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Applied Mathematics

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Geometry

Study anywhere. Anytime. Across all devices.

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