Section 4.2 – Multiplying Matrices Day 2 Algebra 2 Unit 3 – Chapter 4 Section 4.2 – Multiplying Matrices Day 2

MATRICES ROWS NAME COLUMNS

MATRICES Labeling Elements

MATRIX MULTIPLICATION The order in which you list the matrices does matter. The column dimension of the first matrix must equal the row dimension of the second matrix. The row dimension of the first matrix and column dimension of the second matrix determine the size of the product matrix.

MATRIX MULTIPLICATION State the dimensions of each matrix. Can we multiply A x B? Can we multiply B x A? 2 x 2 2 x 3 YES NO

MATRIX MULTIPLICATION You always multiply a row by a column. The result will be a new element. Our result of 16 will be new element c11, because it was a combination of row 1 and column 1 of our two matrices that are being multiplied together.

MATRIX MULTIPLICATION You always multiply a row by a column. The result will be a new element. Our result of 26 will be new element c21, because it was a combination of row 2 and column 1 of our two matrices that are being multiplied together.

MATRIX MULTIPLICATION To finish the problem, repeat the process multiplying row 1 and 2 of matrix A, with rows 2 and 3 of matrix B. Element c12 = 3●6 + 2●3 = 24 Element c13 = 3●7 + 2●8 = 37 Element c22 = 4●6 + 5●3 = 39 Element c23 = 4●7 + 5●8 = 68

MATRIX MULTIPLICATION Finish the problem by placing the final product’s elements into their correct location.

MATRIX MULTIPLICATION BLOCK METHOD MULTIPLY MULTIPLY 37

MATRIX MULTIPLICATION BLOCK METHOD MULTIPLY MULTIPLY 37 21

MATRIX MULTIPLICATION BLOCK METHOD MULTIPLY MULTIPLY 37 21 2

MATRIX MULTIPLICATION BLOCK METHOD MULTIPLY MULTIPLY 37 21 2 -14

MATRIX MULTIPLICATION BLOCK METHOD 37 21 2 -14

GUIDED PRACTICE 1. Find AB if A = and B = –3 3 1 –2 1 5 –3 –2 ANSWER –12 –21 7 9

GUIDED PRACTICE Using the given matrices, evaluate the expression. A = –1 2 –3 0 4 1 , B = 3 2 –2 –1 , C = –4 5 1 0 2. A(B – C) 3. AB – AC 4. (AB) –1 2 ANSWER ANSWER ANSWER 3.5 2 4.5 3 –5 –3.5 –13 1 –21 9 25 –13 –13 1 –21 9 25 –13

Multiplying Matrices Practice #1 PARTNER PRACTICE Multiplying Matrices Practice #1

HOMEWORK Page 211 – 212 #11 – 33 ODD