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Chapter 2: Q9E (page 71)

Interpret the following linear transformation geometrically:

T(x鈫�)=[1011]x鈫�

Short Answer

Expert verified

The image consists of vectors 11,02. It shows vertical shear.

Step by step solution

01

Step1: Linear transformation

We have given T is linear transformation with

Tx鈫�=1011x鈫�

For sketching the image of transformation we will do this by,

10111002=1012

02

Geometrically interoperation  

03

Description of image

In the image of this linear transformation, it is rotated by the angle in the anticlockwise direction.

And the vertical remains the same

04

Final answer

The image consists of vectors 11,02. It shows vertical shear.

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Most popular questions from this chapter

TRUE OR FALSE?

There exists a real number k such that the matrix[k-1-2-4k-3] fails to be invertible.

TRUE OR FALSE?

If the linear system A2x鈫�=b鈫� is consistent, then the systemrole="math" localid="1659352762883" Ax鈫�=b鈫� must be consistent as well.

a. Show that if an invertible n脳nmatrix A admits an LU-factorization, then it admits an LDU factorization. See Exercise 90 d.

b. Show that if an invertible matrix A admits an L DU-factorization, then this factorization is unique. Hint: Suppose that A=L1D1U1=L2D2U2, then U2U-1=D2-1L2-1L1D1is diagonal (why?). Conclude that U2=U1.

Find the matrices of the transformations Tand Ldefined in Exercise 80.

For which values of the constant k is the following matrix invertible?

[11112k14k2]
See all solutions

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