8.4 Matrix Operations Day 1 Thurs May 7 Do Now Solve X – 2y = -6 3x + 4y = 7

8.4 Matrix OperationsDay 1 Thurs May 7

Do NowSolve

X – 2y = -63x + 4y = 7

Matrices

• A matrix is an organization of numbers in a rectangular form

Matrices

• The rows of a matrix are horizontal• The columns are vertical• A matrix with m rows and n columns is said to

be of order m x n• The numbers in a matrix are called entries• The main diagonal starts from the top left and

travels down and to the right

Matrix Operations

• Matrix Addition and Subtraction• Scalar Multiplication• Matrix Multiplication

Matrix Addition and Subtraction

• Given Matrix A and B with the same order

• A + B = add corresponding entries

• A – B = subtract corresponding entries

Ex

• Find A + B for

Ex

• Find C – D for

You try

• Find A + B for

Additive Inverse

• The additive inverse of a matrix is obtained by replacing each entry with its opposite

Ex

• Find –A and A + (-A) given

Scalar Multiplication

• The scalar product of a number k and a matrix A is the matrix kA, obtained by multiplying each entry of A by the number k

Ex

• Find 3A and (-1)A for

Ex

• P.716

Matrix Multiplication

• When multiplying 2 matrices, there is a prerequisite that must be satisfied, or it cannot happen

• Matrix:• Dimensions:• The two inside dimensions must be equal, or

the multiplication is not defined• Note: Just because AB exists, doesn’t mean

that BA also exists

Can we multiply these matrices?

• 1)

• 2)

• 3)

Multiplying Matrices

• To multiply, take the 1st row of matrix A and the 1st column of Matrix B– Multiply each corresponding element, and

then add them together to get each new element

Ex

• Let

• Find• 1) AB• 2) BA• 3) BC• 4) AC

Closure

• Multiply AB given

• HW: p.720 #1-27 odds

8.4 Matrix OperationsDay 2 Fri May 8

• Do Now• Find AB given

HW Review: p.720 #1-27

Properties of Matrix Multiplication

• A(BC) = (AB)C• A(B + C) = AB + AC• (B + C)A = BA + CA

• Note that property 2 and 3 result in different matrices

Word problems

• When constructing a matrix from a word problem, the rows and columns should represent different types of the same thing (rows: types of cookies) (columns: amount of sugar)

Ex7

• P.718

Matrix Equations

• We can write a system of equations into a matrix equation by making each column equivalent to a variable

Ex

• Write the following system into a matrix equation

4x + 2y – z = 39x + z = 54x + 5y – 2z = 1

Closure

• What must be true when multiplying matrices? Adding matrices?

• HW: p.720 #29-45 odds