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In this lesson, we will learn how to multiply matrices.
Q1:
Suppose the matrix product 𝐴 𝐵 𝐶 makes sense. We also know that 𝐴 has 2 rows, 𝐶 has 3 columns, and 𝐵 has 4 entries. Is it possible to determine the possible sizes of these matrices? If so, what are the possible sizes of 𝐴 , 𝐵 , and 𝐶 ?
Q2:
Find the matrices 𝐽 and 𝐾 such that, for any 2 × 3 matrix 𝑋 , 𝐽 𝑋 = 𝑋 and 𝑋 𝐾 = 𝑋 . Explain why 𝐽 and 𝐾 are not the same.
Q3:
Suppose 𝐴 = 1 1 − 1 0 − 2 1 , 𝐵 = − 2 1 − 3 0 , 𝐶 = 0 − 2 3 1 1 0 . a n d Which of the following products is defined?
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