University:
The University Of Western Ontario
Course:
CALC 1000A | Calculus I
Academic year:

2020
Views:

461

Pages:

3
Author:

Kyuwon J.

Matrices 1. What is a Matrix? A matrix is a rectangular array of numbers arranged in rows and columns. Each number in a matrix is called an element. Example: 1 2 3 A= 4 5 6 - A is a 2 × 3 matrix (2 rows and 3 columns). 2. Matrix Operations 2.1 Matrix Addition To add two matrices, they must have the same dimensions. Add corresponding elements. Example: 1 2 5 6 A= ,B= 3 4 7 8 1+5 2+6 6 8 A+B = = 3+7 4+8 10 12 2.2 Matrix Subtraction Subtract corresponding elements of two matrices with the same dimensions. Example: 1−5 2−6 −4 −4 A−B = = 3−7 4−8 −4 −4 2.3 Matrix Multiplication To multiply matrices: 1. The number of columns in the first matrix must equal the number of rows in the second matrix. 2. Multiply rows of the first matrix by columns of the second and sum the products. Example: 1 2 5 6 A= ,B= 3 4 7 8 (1 · 5 + 2 · 7) (1 · 6 + 2 · 8) A×B = (3 · 5 + 4 · 7) (3 · 6 + 4 · 8) 1 19 22 = 43 50 3. Practice Problems Problem 1: Matrix Addition Given: 2 3 4 1 −1 0 A= ,B= 1 0 −1 −2 4 3 Find A + B. Solution: 2+1 3 + (−1) 4 + 0 3 2 4 A+B = = 1 + (−2) 0+4 −1 + 3 −1 4 2 Problem 2: Matrix Subtraction Given: 7 5 4 2 A= ,B= 3 2 1 0 Find A − B. Solution: 7−4 5−2 3 3 A−B = = 3−1 2−0 2 2 Problem 3: Matrix Multiplication Given: 2 3 1 0 A= ,B= 1 4 5 6 Find A × B. Solution: (2 · 1 + 3 · 5) (2 · 0 + 3 · 6) 17 18 A×B = = (1 · 1 + 4 · 5) (1 · 0 + 4 · 6) 21 24 Problem 4: Dimensions Check Can the following matrices be multiplied? 1 2 5 6 7 A= ,B= 3 4 8 9 10 2 Solution: Matrix A is 2 × 2, and B is 2 × 3. Since the number of columns in A equals the number of rows in B, they can be multiplied. The resulting matrix will have dimensions 2 × 3. Problem 5: Scalar Multiplication 2 4 If C = and k = 3, find k · C. 6 8 Solution: 3·2 3·4 6 12 k·C = = 3·6 3·8 18 24 3