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Chapter 2: Q11E (page 85)

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

11.[123][321]

Short Answer

Expert verified

Product of given matrix is.[10]

Step by step solution

01

Step1:Matrix multiplication

If A is matrix of ordern脳pand 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�)T(x鈫�)=B(Ax鈫�)

02

 Step2: Assuming the matrix

Let the given matrix.

A=[123],B=[321]

Order of Matrix Ais1脳3, and order of matrixB is.3脳1

Since,.3=3 Thus, the product is defined.

03

Multiplication of matrix

Now, find the product as follows:

AB=[123][321]=[1.3+2.2+3.1]=[10]

Hence, the product of the given matrix is.[10]

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Most popular questions from this chapter

Consider the transformation Tfrom R2to role="math" localid="1659714471562" R2that rotates any vector x鈫�through a given angle胃in the counterclockwise direction. Compare this with Exercise 33. You are told that Tis linear. Find the matrix of Tin terms of胃.

In the financial pages of a newspaper, one can sometimes find a table (or matrix) listing the exchange rates between currencies. In this exercise we will consider a miniature version of such a table, involving only the Canadian dollar (C\() and the South African Rand (ZAR) . Consider the matrix

role="math" localid="1659786495324" C\)ZARA=[11/881]C\(ZAR

representing the fact thatrole="math" localid="1659786520551" C\)1 is worth role="math" localid="1659786525050" ZAR8 (as of September 2012).

a. After a trip you have C$100 and ZAR1,600 in your pocket. We represent these two values in the vector x鈫�=[1001,600] . Compute Ax鈫� . What is the practical significance of the two components of the vector Ax鈫� ?

b. Verify that matrix A fails to be invertible. For which vectorsb鈫�is the system Ax鈫�=b鈫� consistent? What is the practical significance of your answer? If the system Ax鈫�=b鈫� is consistent, how many solutionsx鈫�are there? Again, what is the practical significance of the answer?

TRUE OR FALSE?

Matrix(111101110) is invertible.

Consider the transformation T from R2to R2that rotates any vectorx鈫�through an angle of 45掳in the counterclockwise direction, as shown in the following figure:

You are told that T is a linear transformation. (This will be shown in the next section.) Find the matrix of T .

The function T[xy]=[x-yy-x]is a linear transformation?
See all solutions

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