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Chapter 2: Q45E (page 74)

A matrix of the formA=[abb鈭�a] ,wherea2+b2=1represents a reflection about a line. See Exercise17 .Use the formula derived inExercise2.1.13 tofind the inverse of A. Explain.

Short Answer

Expert verified

The inverse of the matrix is,A鈭�1=A=(abb鈭�a)

Step by step solution

01

Consider the matrix 

Consider the matrix.

A=(abb鈭�a)

The standard formula is,

A=(abcd)鈬�A鈭�1=1ad鈭�bc(d鈭�b鈭�ca)

02

Compute and Interpret the inverse matrix 

The inverse of the matrix is,

A鈭�1=1鈭�a脳a鈭�b脳鈭�b(鈭�a鈭�b鈭�ba)鈭�A鈭�1=1鈭�(a2+b2)(鈭�a鈭�b鈭�ba)

Substitute the given value, a2+b2=1

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Most popular questions from this chapter

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(x)鈫�=Ax鈫�on this face.

26.[0110]

Which of the functionsf fromR toR in Exercises 21 through 24 are invertible?21 f(x)=x2.

Is the product of two lower triangular matrices a lower triangular matrix as well? Explain your answer.

Question:

  1. If Ais any 3x3 transition matrix (see Definition 2.1.4), find the matrix product [111]A .
  2. For a fixed n , let e鈫� be the row vector e鈫�=[1,1,..,1]n1's . Show that an nxn matrix A with nonnegative entries is a transition matrixif (and only if)e鈫�A=e鈫� .

TRUE OR FALSE?

If A is an invertible2脳2 matrix and B is any 2脳2 matrix, then the formula rref (AB) = rref (B)must hold.

See all solutions

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