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

TRUE OR FALSE?

There exists an invertible $10 \times 10$ matrix that has 92 ones among its entries.

The statement is false.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Consider the parameters

A matrix will be non-invertible if it has identical rows.

An inverse of a matrix has an order, $10 \times 10$

The number of ones in inverse matrix, 92

A matrix will have 100 entries. If 92 among them are ones, then, there will be identical rows. Such identical rows cancel out each other. Then, the inverse of that matrix will not exist.

Step 2: Conclusion

Hence, the given statement is false.

Most popular questions for Math Textbooks

Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformation $T \vec{(x)} = A \vec{x}$ on this face.

24. $[\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]$

Let’s revisit the mini-Web with the graph

$\begin{matrix} 1 & ⇄ & 2 \\ ↓ & ↙ & ↑ \\ 3 & \to & 4 \end{matrix}$

But here we consider the surfing model with a “jumping rate” of 20%, as discussed in Exercise 2.1.53. The corresponding transition matrix is

. $B = [\begin{matrix} 0 .05 & 0 .45 & 0 .05 & 0 .05 \\ 0 .45 & 0 .05 & 0 .05 & 0 .85 \\ 0 .45 & 0 .45 & 0 .05 & 0 .05 \\ 0 .05 & 0 .05 & 0 .85 & 0 .05 \end{matrix}]$

This transition matrix is positive and therefore regular, so that Theorem 2.3.11 applies. Use the power method (see Exercise 76) to find the equilibrium distribution. You may use technology. Write the components of ${\vec{x}}_{e q u}$ as rational numbers.

Consider the regular tetrahedron sketched below, whose center is at the

origin.

Let T from $ℝ^{3}$ to $ℝ^{3}$ be the rotation about the axis through the points 0 and $P_{2}$ that transforms $P_{1}$ into $P_{3}$ . Find the images of the four corners of the tetrahedron under this transformation.

$P_{0} \overset{r}{\to} P_{1} \underset{}{\to} P_{3} P_{2} \underset{}{\to} P_{3} \underset{}{\to}$

Let L from $ℝ^{3}$ to $ℝ^{3}$ be the reflection about the plane through the points 0 , $p_{0} and p_{3}$ . Find the images of the four corners of the tetrahedron under this transformation.

$P_{0} \overset{L}{\to} P_{1} \overset{}{\to} P_{2} \overset{}{\to} P_{3} \overset{}{\to}$

Describe the transformations in parts (a) through (c) geometrically.

$a . T^{- 1} b . L^{- 1} c . T^{2} = T \circ T (t h e c o m p o s i t e o f T w i t h i t s e l f)$

d. Find the images of the four corners under the transformations $T \circ L a n d L \circ T$ . Are the two transformations the same?

$P_{0} \overset{T \circ L}{\to} P_{0} \overset{T \circ L}{\to} P_{1} \overset{}{\to} P_{1} \overset{}{\to} P_{2} \overset{}{\to} P_{2} \overset{}{\to} P_{3} \overset{}{\to} P_{3} \overset{}{\to}$

e. Find the images of the four corners under the transformation $L \circ T \circ L$ . Describe this transformation geometrically

TRUE OR FALSE?

The function $T [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} {(y + 1)}^{2} & {(y - 1)}^{2} \\ {(x - 3)}^{2} & {(x + 3)}^{2} \end{matrix}]$ is a linear transformation.

Find all 2 × 2 matrices X such that AX = X A for all 2 × 2 matrices A.

Want to see more solutions like these?

Get Started - It’s free

Find Study Materials for

Create Study Materials

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

TRUE OR FALSE?

There exists an invertible $10 \times 10$ matrix that has 92 ones among its entries.

Step by Step Solution

Step 1: Consider the parameters

Step 2: Conclusion

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

TRUE OR FALSE? There exists an invertible 10×10 matrix that has 92 ones among its entries.

Step by Step Solution

Step 1: Consider the parameters

Step 2: Conclusion

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

TRUE OR FALSE?

There exists an invertible $10 \times 10$ matrix that has 92 ones among its entries.