Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

a. Find $(\begin{matrix} 2 & 3 \\ 4 & 5 \\ 6 & 7 \end{matrix}) + (\begin{matrix} 7 & 5 \\ 3 & 1 \\ 0 & - 1 \end{matrix})$
b. Find $9 (\begin{matrix} 1 & - 1 & 2 \\ 3 & 4 & 5 \end{matrix})$

a. The value of $(\begin{matrix} 2 & 3 \\ 4 & 5 \\ 6 & 7 \end{matrix}) + (\begin{matrix} 7 & 5 \\ 3 & 1 \\ 0 & - 1 \end{matrix})$ is $(\begin{matrix} 9 & 8 \\ 7 & 6 \\ 6 & 6 \end{matrix})$

b. The value of $9 (\begin{matrix} 1 & - 1 & 2 \\ 3 & 4 & 5 \end{matrix})$ is $(\begin{matrix} 9 & - 9 & 18 \\ 27 & 36 & 45 \end{matrix})$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Consider the matrices and perform the addition operation.

If A and B are the matrices of same size, then, the sum of matrices is,

$[\begin{matrix} a_{11} & \dots & a_{1 m} \\ ⋮ & ⋮ \\ a_{n 1} & \dots & a n m \end{matrix}] + [\begin{matrix} b_{11} & \dots & b_{1 m} \\ ⋮ & ⋮ \\ b_{n 1} & \dots & b n m \end{matrix}] = [\begin{matrix} a_{11} & + b_{11} & \dots a_{1 m} & + b_{1 m} \\ ⋮ & ⋮ \\ a_{n 1} & + b_{n 1} & \dots a_{n m} & b_{n m} \end{matrix}]$

The given matrices are,

$(\begin{matrix} 2 & 3 \\ 4 & 5 \\ 6 & 7 \end{matrix}) + (\begin{matrix} 7 & 5 \\ 3 & 1 \\ 0 & - 1 \end{matrix})$

Perform the addition operation.

$= (\begin{matrix} 2 + 7 & 3 + 5 \\ 4 + 3 & 5 + 1 \\ 6 + 0 & 7 + (- 1) \end{matrix})$

$= (\begin{matrix} 9 & 8 \\ 7 & 6 \\ 6 & 6 \end{matrix})$

Step 3: Consider the matrix and perform the product operation.

If A is an $n \times m$ matrix with row vectors $\vec{ω 1}, . . . . . ., \vec{ω n}$ and $\vec{x}$ is a vector in $ℝ^{m}$ then,

$A \vec{x} = [\begin{matrix} - \vec{ω 1} - \\ ⋮ \\ - \vec{ω n} - \end{matrix}] \vec{x} = [\begin{matrix} - \vec{ω 1} . \vec{x} - \\ ⋮ \\ - \vec{ω n} . \vec{x} - \end{matrix}]$

The given matrix is,

$9 (\begin{matrix} 1 & - 1 & 2 \\ 3 & 4 & 5 \end{matrix})$

Here A is $(\begin{matrix} 1 & - 1 & 2 \\ 3 & 4 & 5 \end{matrix})$ and $\vec{x}$ is 9

Perform the row column operation.

localid="1659341013254" $\begin{array}{l} = (\begin{matrix} 9.1 & 9 (- 1) & 9.2 \\ 9.3 & 9.4 & 9.5 \end{matrix}) \\ = (\begin{matrix} 9 & - 9 & 18 \\ 27 & 36 & 45 \end{matrix}) \end{array}$

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Linear Algebra With Applications

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Short Answer

a. Find $(\begin{matrix} 2 & 3 \\ 4 & 5 \\ 6 & 7 \end{matrix}) + (\begin{matrix} 7 & 5 \\ 3 & 1 \\ 0 & - 1 \end{matrix})$
b. Find $9 (\begin{matrix} 1 & - 1 & 2 \\ 3 & 4 & 5 \end{matrix})$

Step by Step Solution

Step 1: Consider the matrices and perform the addition operation.

Step 3: Consider the matrix and perform the product operation.

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Linear Algebra With Applications

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Short Answer

a. Find (234567)+(75310-1)b. Find 9(1-12345)

Step by Step Solution

Step 1: Consider the matrices and perform the addition operation.

Step 3: Consider the matrix and perform the product operation.

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a. Find $(\begin{matrix} 2 & 3 \\ 4 & 5 \\ 6 & 7 \end{matrix}) + (\begin{matrix} 7 & 5 \\ 3 & 1 \\ 0 & - 1 \end{matrix})$
b. Find $9 (\begin{matrix} 1 & - 1 & 2 \\ 3 & 4 & 5 \end{matrix})$