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3 cards from this section. Quick, good the night before a test.
Is matrix multiplication commutative? Give an example.
Think about multiplying two matrices and their orders.
What is the product of a 2x3 matrix and a 3x2 matrix called?
Recall the resulting dimensions based on matrix multiplication rules.
Is matrix multiplication commutative?
Think of a basic example to illustrate.
If A is a 3x2 matrix and B is a 2x4 matrix, what will be the dimensions of the resulting matrix AB?
Focus on the outer rows and columns of A and B.
Prove that matrix multiplication is associative. Let A, B, and C be matrices of compatible dimensions.
Start with the definition of matrix multiplication and examine the resulting elements.
If A is a 2x2 matrix and B is a 2x3 matrix, derive the general formula for the elements of the product AB.
Remember how to compute dot products for each row and column.
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