Example 1 · level 1
A = [8, 7; −3, 9] and B = [−4, −3; 3, −1] (rows separated by semicolons). Find the entry in row 1, column 2 of 3A + B.
Show solution
- Required entry = 3 × 7 + 1 × (−3) = 18.
Answer: 18
CLASS 12 MATHS · MATRICES
Matrix addition, scalar multiple and product
Add matrices entry by entry. In a product AB, the (i, j) entry is row i of A times column j of B: multiply matching entries and add.
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Worked examples
Example 2 · level 2
A = [5, 5; 5, 5] is 2 × 2 and B = [0, 2; 5, 0] is 2 × 2 (rows separated by semicolons). Find the entry in row 2, column 1 of AB.
Show solution
- (AB)21 = 5 × 0 + 5 × 5
- = 0 + 25 = 25.
Answer: 25
Example 3 · level 3
A = [−1, 4, 4; −1, 4, −3] is 2 × 3 and B = [3, −3; −1, 5; −1, 5] is 3 × 2 (rows separated by semicolons). Find the entry in row 1, column 1 of AB.
Show solution
- (AB)11 = −1 × 3 + 4 × (−1) + 4 × (−1)
- = (−3) + (−4) + (−4) = −11.
Answer: -11