
- (a) We can multiply two matrices only if the number of __________ in the first matrix is the same as the number of __________ in the second matrix.
- (b) If A is a 3 × 3 matrix and B is a 4 × 3 matrix, which of the following matrix multiplications are possible?
- (i) AB
- (ii) BA
- (iii) AA
- (iv) BB
(a)

To fill: The condition to multiply two matrices.
Answer to Problem 2E
To multiply two matrices, number of columns in first matrix is same as the number of rows in second matrix.
Explanation of Solution
When the number of columns of first matrix is same as the number of rows of second matrix they have the equal number of entries to multiply.
Thus, to multiply two matrices, number of columns in first matrix should be same as the number of rows in second matrix.
(b)

The condition to multiply two matrices of different dimensions.
Answer to Problem 2E
The possible matrix multiplication is BA and AA.
Explanation of Solution
Given:
The dimension of matrix A is a
The number of columns of matrix B is 3 and the number of rows of matrix A is 3 which is equal and this is required for multiplication.
So the matrix multiplication BA is possible.
And another matrix multiplication of AA is possible because number of columns and number of rows of matrix A is same.
Thus, the possible matrix multiplication is BA and AA.
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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