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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