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Chapter 2: Q9E (page 85)

If possible, compute the matrix products in Exercises 1 through 13, using paper and pencil.

9.[1224][-683-4]

Short Answer

Expert verified

The product of given matrix is .[0000]

Step by step solution

01

Step1:Matrix multiplication 

If A is matrix of ordern脳pand B is matrix of order.m脳q Then the matrix multiplication ofABIs defined only if.p=m

If Bis adata-custom-editor="chemistry" m脳q matrix and A n脳pmatrix, then the product BAis defined as the matrix of the linear transformation .T(x鈫�)=B(Ax鈫�)

02

Assuming the matrix 

Let the given matrix

A=[1224],B=[鈭�683鈭�4]

Order of MatrixAis2脳2and order of matrixBis2脳2.

Since .2=2Thus the product is define.

03

Multiplication of matrix

Now, find the product as follows:

AB=[1.(鈭�6)+2.31.8+2.(鈭�4)2.(鈭�6)+4.32.8+4.(鈭�4)]=[0000]

Hence, the product of given matrix is .[0000]

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Most popular questions from this chapter

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.

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: Show that if A and B are nxn transition matrices, then AB will be a transition matrix as well. Hint: Use Exercise 67b.

TRUE OR FALSE?

If A2=In, then matrixAmust be invertible.

TRUE OR FALSE?

The matrix(111-1) represents a reflection about a line.

See all solutions

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