Matrix Addition and Subtraction
In order to add or subtract matrices, the dimensions of each matrix must be the same. If the dimensions are not the same, the sum or difference is undefined. Then, you add or subtract the matching numbers in the two matrices.
1. [2 -4 6 + [9 -3 -8 = [11 -7 -2
4 9 -7] 0 -2 5] 4 7 -2]
2. [ 4 -12 5 - [-4 -5 -13 = [8 -7 18
-2 -34 3] -3 15 12] 1 -49 -9]
Matrix Multiplication
To multiply two matrices, the number of columns in the first matrix must be the same as the number of rows in the second in order to multiply. For example a 2x3 matrix and a 3x4 matrix can be multiplied because the inside numbers are the same.
Once you know you can multiply, you then multiply each number in the first row by each number in the first column and add the products together. You do this for each row and each column.
1. [-2 5 -3 [-2 5
1 -4 -2] x 5 -2
-3 -1]
This is a 2x3 and 3x2, so you can multiply.
=[(-2)(-2) + (5)(5) + (-3)(-3) (-2)(5) + (5)(-2) + (-3)(-1)
(1)(-2) + (-4)(5) + (-2)(-3) (1)(5) + (-4)(-2) + (-2)(-1)]
=[ 4+25+9 -10-10+3
-2-20+6 5+8+2]
=[38 -17
-16 15]
Love, Jenna
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