4-2 ADDING and SUBTRACTING MATRICES (P. 170-176)

4-2 ADDING AND SUBTRACTING MATRICES (p. 170-176)

Sometimes you add or subtract matrices to get new information.

You can perform matrix addition or subtraction on matrices with equal dimensions by adding or subtracting the corresponding elements. Corresponding elements are those elements that are in the same position in each matrix.

Example: The following table shows information on the number of ticket sales for a brand new movie that is showing at two different theatres.

Matinee Matinee Evening Evening Theatre Children Adults Children Adults 1 198 350 54 439 2 201 375 58 386

Write two 2 2 matrices to represent the number of ticket sales from the above table, one matrix for matinee sales and one for evening sales. Label the rows and columns for each matrix.

? ? ? ? M =   E =   ? ? ? ?

Find the combined ticket sales for the two showings. In other words, add the two matrices. Label the rows and columns for the combined matrix.

Do 1b on p. 171.

Matrix addition is summarized in the table on p. 171. Emphasize same dimensions and the adding of corresponding elements.

A zero matrix is a matrix where all of its elements are zero.

Example: What is the zero matrix for a 3 4 matrix?

The additive inverse or opposite of a matrix is a matrix whose elements are the opposites of the corresponding elements of the other matrix.

Example: Find the sum  3  8  3 8         5 1   5 1

Do 2 on p. 171. On p. 171, note that some of the properties of real number addition also apply to matrix addition. Briefly discuss these properties.

You can define matrix subtraction by using the Additive Inverse Property for matrices. That is, if you subtract one matrix from another matrix, you get the same answer if you had added the opposite of the matrix to the other matrix. For real numbers, 7 – 4 = 7 + (-4).

Example: Find the difference  4 8  7  9        2 0  5 6 

Do you think that matrix subtraction is commutative? Why or why not?

A matrix equation is an equation in which the variable is a matrix. You can use the addition and subtraction properties of equality to solve matrix equations. You basically isolate the variable, just like solving simpler equations.

Example: Solve the matrix equation for the matrix X. 2 5  10  3     X - 3 -1   4 9  8 - 2  6  9

Do 4 on p. 173.

Equal matrices are matrices with the same dimensions and equal corresponding elements.

Example: Are these two matrices equal? 27 -16 5   3 - 4 - 20   P  Q  9 4 -.25    8  40 - 3 8   - 5  2 64   .2 

Do 5a,b on p. 173.

Example: Solve the equation for m and n. Since the matrices are equal, their corresponding elements are equal.

2m - n - 3  15 m  n       8 - 4m  2n  8 - 30 

Do 6b on p. 173. Homework: p. 174-176: 3,9,11,14,17,19,21,23a,b,25,27,28b,31,36,40,43

27a. Plant 1 Plant 2 Plastic Rubber Plastic Rubber 1-color 1000 1400 1-color 1200 3600 3-color 2600 3800 3-color 1800 4800