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Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 1: Q14E (page 35)

Compute the products Axin Exercises 13 through 15 using
paper and pencil. In each case, compute the product
two ways: in terms of the columns of A and in terms of the rows of A.
14.
$[\begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \end{matrix}] [\begin{matrix} - 1 \\ 2 \\ 1 \end{matrix}]$

Short Answer

Expert verified

The dot product $A x^{鈫�} of [\begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \end{matrix}] [\begin{matrix} - 1 \\ 2 \\ 1 \end{matrix}] is [\begin{matrix} 6 \\ 8 \end{matrix}]$

Step by step solution

01

Step 1:

Find $A x .$ in terms of rows of A.

$[\begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \end{matrix}] [\begin{matrix} - 1 \\ 2 \\ 1 \end{matrix}]$

$鈬� [\begin{matrix} (1) (- 1) + (2) (2) + (3) (1) \\ (2) (- 1) + (3) (2) + (4) (1) \end{matrix}] 鈬� [\begin{matrix} - 1 + 4 + 3 \\ - 2 + 6 + 4 \end{matrix}] 鈬� [\begin{matrix} 6 \\ 8 \end{matrix}]$

02

Step 2:

Find $A x .$ in terms of columns of A.

$[\begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \end{matrix}] [\begin{matrix} - 1 \\ 2 \\ 1 \end{matrix}]$

$鈬� - 1 [\begin{matrix} 1 \\ 2 \end{matrix}] + 2 [\begin{matrix} 2 \\ 3 \end{matrix}] + 1 [\begin{matrix} 3 \\ 4 \end{matrix}] 鈬� [\begin{matrix} - 1 + 4 + 3 \\ - 2 + 6 + 4 \end{matrix}] 鈬� [\begin{matrix} 6 \\ 8 \end{matrix}]$

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Most popular questions from this chapter

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