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Chapter 1: Q51E (page 37)

Consider an n脳 mmatrix A, an r脳 smatrix B, and a vectorx鈫�in鈩�p. For which values of n, m, r,s, and pis the productA(Bx鈫�)defined?

Short Answer

Expert verified

The values of n, m, r, s and p is the product of ABx鈫�is defined are s = p and m = r

Step by step solution

01

Find the solutions of the systems

For m=rto be defined the number of columns of B must be equal the number of components ofx鈫�.

So columns of B are [s] components ofx鈫�is p

For ABx鈫�to be defined we must have m=r

02

Final answer:

The values of n, m, r, s and p is the product ofABx鈫� is defined are s = p and m = r

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Most popular questions from this chapter

Let A be a 4 脳 4 matrix, and letb鈫�andc鈫� be two vectors in鈩�4 . We are told that the systemAx鈫�=b鈫� has a unique solution. What can you say about the number of solutions of the systemAx鈫�=c鈫� ?

Compute the products Axin Exercises 13 through 15 using

paper and pencil. In each case, compute the product

two ways: in terms of the columns of A and in terms of the rows of A.

14.

[123234][-121]

If Aand Sare invertible nxnmatrices, then matrices AandSTASmust be similar.

Ifis a symmetric matrix, what can you say about the definiteness ofA2? When isA2 positive definite?

The system is[123456000]x鈫�=[123]inconsistent
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