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Chapter 2: Q38E (page 108)

If A and B are two 4 脳 3 matrices such thatAv鈫�=Bv鈫� for all vectorsv鈫� in鈩�3 , then matrices A and B must be equal.

Short Answer

Expert verified

The statement is true.

Step by step solution

01

Explaining

The claim is that if A and B are two 4x3 matrices such that Av鈫�=Bv鈫� forv鈫� all then A = B .

02

Result

If the statement holds for allv鈫� there is no way thatAv鈫�=Bv鈫� unless A=B. Thus the statement must be true.

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Most popular questions from this chapter

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

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�.

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TRUE OR FALSE?

Matrix [1236] is invertible.

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