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Chapter 2: Q54E (page 109)

TRUE OR FALSE?

The formula rref(AB) =rref(A)rref(B)holds for alln脳p matrices A and for allp脳m matrices.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Reduce row echelon form

The reduced row echelon form of a matrix contains leading ones followed by zeros in each row with a shift in place of leading ones with every next row.

02

Consider the parameters

The product of rref of matrices will result in either identity matrix or the identity matrix followed by rows of zeros.

Thus, the formula rref(AB) = rref (A) rref(B) holds good.

Hence, the statement is true.

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Most popular questions from this chapter

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

origin.

Let T from 鈩�3to 鈩�3be the rotation about the axis through the points 0 and P2that transforms P1 into P3. Find the images of the four corners of the tetrahedron under this transformation.

P0鈫�rP1鈫�P3P2鈫�P3鈫�

Let L from 鈩�3to 鈩�3be the reflection about the plane through the points 0 , p0andp3. Find the images of the four corners of the tetrahedron under this transformation.

P0鈫�LP1鈫�P2鈫�P3鈫�

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

a.T-1b.L-1c.T2=T鈭�T鈥�(thecompositeofTwithitself)

d. Find the images of the four corners under the transformations T鈭�LandL鈭�T. Are the two transformations the same?

P0鈫�T鈭�LP0鈫�T鈭�LP1鈫�P1鈫�P2鈫�P2鈫�P3鈫�P3鈫�

e. Find the images of the four corners under the transformation L鈭�T鈭�L. Describe this transformation geometrically

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?

Matrix(111101110) is invertible.

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

TRUE OR FALSE?

If a matrixA=(abcd) represents the orthogonal projection onto a line L , then the equationa2+b2+c2+d2=1must hold.

See all solutions

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