Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

Answers without the blur.

Just sign up for free and you're in.

Short Answer

In Exercises 25 through 30, find the matrix B of the linear transformation $T (\vec{x}) = A (\vec{x})$ with respect to the basis $J = ({\vec{v}}_{1}, \dots . ., {\vec{v}}_{m})$ .
$A = (\begin{matrix} 0 & 1 \\ 2 & 3 \end{matrix}); {\vec{v}}_{1} = [\begin{matrix} 1 \\ 2 \end{matrix}], {\vec{v}}_{2} = [\begin{matrix} 1 \\ 1 \end{matrix}]$

The matrix is, $B = (\begin{matrix} 6 & 4 \\ - 4 & 3 \end{matrix})$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Consider the vectors.

The matrix and vectors are,

$A = (\begin{matrix} 0 & 1 \\ 2 & 3 \end{matrix}); {\vec{v}}_{1} = [\begin{matrix} 1 \\ 2 \end{matrix}], {\vec{v}}_{2} = [\begin{matrix} 1 \\ 1 \end{matrix}]$

Step 2: Compute the matrix using formula.

The formula is, $B = S^{- 1} A S$ .

Compute the matrix S

The inverse of the matrix is,

$S = (\begin{matrix} a & b \\ c & d \end{matrix}) \Rightarrow S^{- 1} = \frac{1}{a d - b c} (\begin{matrix} d & - b \\ - c & a \end{matrix})$

For S put the values.

role="math" $S = ({\vec{v}}_{1}, {\vec{v}}_{2}) = (\begin{matrix} 1 & 1 \\ 2 & 1 \end{matrix}) \Rightarrow S^{- 1} = \frac{1}{- 1} (\begin{matrix} 1 & - 1 \\ - 2 & 1 \end{matrix})$

Substitute these values in the formula.

$B = S^{- 1} A S \Rightarrow B = \frac{1}{- 1} (\begin{matrix} 1 & - 1 \\ - 2 & 1 \end{matrix}) (\begin{matrix} 0 & 1 \\ 2 & 3 \end{matrix}) (\begin{matrix} 1 & 1 \\ 2 & 1 \end{matrix}) ∴ B = (\begin{matrix} 6 & 4 \\ - 4 & 3 \end{matrix})$

Step 3: Final answer.

The matrix is, $B = (\begin{matrix} 6 & 4 \\ - 4 & 3 \end{matrix})$ .

Find Study Materials for

Create Study Materials

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Consider the vectors.

Step 2: Compute the matrix using formula.

Step 3: Final answer.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

In Exercises 25 through 30, find the matrix B of the linear transformation T(x→)=A(x→) with respect to the basis J=(v→1,…..,v→m). A=(0123);v→1=[12],v→2=[11]

Step by Step Solution

Step 1: Consider the vectors.

Step 2: Compute the matrix using formula.

Step 3: Final answer.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths