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Understand multiplying matrices with detailed examples in Holt Algebra 2 book. Learn to find the product, check dimensions, and calculate entries efficiently. Follow step-by-step instructions for matrix multiplication.
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4-2 Multiplying Matrices Review Holt Algebra 2
An m n matrix A can be identified by using the notation Am n.
Just as you look across the columns of A and down the rows of B to see if a product AB exists, you do the same to find the entries in a matrix product.
Example 2A: Finding the Matrix Product Find the product, if possible. WX Check the dimensions. W is 3 2 , X is 2 3 . WX is defined and is 3 3.
Example 2A Continued Multiply row 1 of W and column 1 of X as shown. Place the result in wx11. 3(4) + –2(5)
Example 2A Continued Multiply row 1 of W and column 2 of X as shown. Place the result in wx12. 3(7) + –2(1)
Example 2A Continued Multiply row 1 of W and column 3 of X as shown. Place the result in wx13. 3(–2) + –2(–1)
Example 2A Continued Multiply row 2 of W and column 1 of X as shown. Place the result in wx21. 1(4) + 0(5)
Example 2A Continued Multiply row 2 of W and column 2 of X as shown. Place the result in wx22. 1(7) + 0(1)
Example 2A Continued Multiply row 2 of W and column 3 of X as shown. Place the result in wx23. 1(–2) + 0(–1)
Example 2A Continued Multiply row 3 of W and column 1 of X as shown. Place the result in wx31. 2(4) + –1(5)
Example 2A Continued Multiply row 3 of W and column 2 of X as shown. Place the result in wx32. 2(7) + –1(1)
Example 2A Continued Multiply row 3 of W and column 3 of X as shown. Place the result in wx33. 2(–2) + –1(–1)