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Chapter 2: Q4E (page 85)

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

4.[1-1-22][7531]

Short Answer

Expert verified

Product of given matrix is.[44鈭�8鈭�8]

Step by step solution

01

Step1:Matrix multiplication

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

If Bis am脳qmatrix and An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=[1鈭�1鈭�22],B=[7531]

Order of Matrix Ais2脳2, and order of matrix Bis.2脳2

Since.2=2 Thus the product is defi ne.

03

Multiplication of matrix

Now, find the product as follows:

AB=[1.7鈭�1.31.5鈭�1.1鈭�2.7+2.3鈭�2.5+2.1]=[44鈭�8鈭�8]

Hence, the product of the given matrix is.[44鈭�8鈭�8]

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Most popular questions from this chapter

Consider two n x nmatrices A and B whose entries are positive or zero. Suppose that all entries of A are less than or equal to 鈥�s鈥�, and all column sums of B are less than or equal to 鈥�r鈥� (the column sum of a matrix is the sum of all the entries in its column). Show that all entries of the matrix AB are less than or equal to 鈥�sr鈥�.

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

Use the formula derived in Exercise 2.1.13to find the inverse of the rotation matrix

localid="1659346816315" A=[肠辞蝉胃-蝉颈苍胃蝉颈苍胃肠辞蝉胃].

Interpret the linear transformation defined by A-1geometrically. Explain.

TRUE OR FALSE?

There exists an upper triangular2脳2 matrixAsuch that A2=(1101) .

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.

24. [0-110]
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