15
QuizMultiple Choice

Scalar and Matrix Multiplication — Quiz

Question 15 • Advanced Algebra: Concepts and Connections

Which matrix multiplication is possible?

Answer
A
the 2 by 1 column matrix row 1 1 row 2 negative 1 times the 1 by 2 row matrix 0 4
B
the 2 by 2 matrix row 1, 1 0 row 2, 1 1 times the 1 by 2 row matrix 3 0
C
the 2 by 1 column matrix row 1 3 row 2 negative 2 times the 2 by 2 matrix, row 1, column 1, negative 1 column 2, 0 row 2, column 1, 0 column 2, 3
D
the 1 by 2 row matrix 0 3 times the 1 by 2 row matrix column 1 1 column 2 negative 4

Explanation

A multiplication is possible when the number of columns in the first matrix equals the number of rows in the second. Choice A has dimensions 2 by 1 and 1 by 2, so the inner dimensions are both 1; the product is defined and has dimensions 2 by 2. The other choices have mismatched inner dimensions.

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