Matrix Operations Monday, August 06, 2018

What is a Matrix? MATRIX: A rectangular arrangement of numbers in rows and columns. The ORDER of a matrix is the number of the rows and columns. The ENTRIES are the numbers in the matrix. This order of this matrix is a 2 x 3. columns rows Monday, August 06, 2018

What is the order? (or square matrix) 3 x 3 (Also called a row matrix) (Also called a column matrix) Monday, August 06, 2018

Adding Two Matrices To add two matrices, they must have the same order. To add, you simply add corresponding entries. Monday, August 06, 2018

= 7 7 4 5 = 7 5 7 Monday, August 06, 2018

Subtracting Two Matrices To subtract two matrices, they must have the same order. You simply subtract corresponding entries. Monday, August 06, 2018

2-0 -4-1 3-8 -5 2 -5 8-3 0-(-1) -7-1 5 -8 1 1-(-4) 5-2 0-7 5 3 -7 = = Monday, August 06, 2018

Multiplying a Matrix by a Scalar In matrix algebra, a real number is often called a SCALAR. To multiply a matrix by a scalar, you multiply each entry in the matrix by that scalar. Monday, August 06, 2018

-3 3 -2 6 -5 -2(-3) -2(3) 6 -6 -12 -2(6) -2(-5) 10 Monday, August 06, 2018

Multiplying Matrices Monday, August 06, 2018

Scalar Multiplication - each element in a matrix is multiplied by a constant. Monday, August 06, 2018

**Multiply rows times columns. **You can only multiply if the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix. They must match. Dimensions: 3 x 2 2 x 3 Monday, August 06, 2018 The dimensions of your answer.

Examples: 2(3) + -1(5) 2(-9) + -1(7) 2(2) + -1(-6) 3(3) + 4(5) 3(-9) + 4(7) 3(2) + 4(-6) Monday, August 06, 2018

*They don’t match so can’t be multiplied together.* Dimensions: 2 x 3 2 x 2 *They don’t match so can’t be multiplied together.* Monday, August 06, 2018

2 x 2 2 x 2 0(4) + (-1)(-2) 0(-3) + (-1)(5) 1(4) + 0(-2) 1(-3) +0(5) *Answer should be a 2 x 2 2 x 2 2 x 2 0(4) + (-1)(-2) 0(-3) + (-1)(5) 1(4) + 0(-2) 1(-3) +0(5) Monday, August 06, 2018