Download Perform Basic Matrix Operations

25. BASIC MATRIX
OPERATIONS
MATRIX
• A matrix is a rectangular array of numbers in rows
and columns.
2
3
−1 8
0 1.2
DIMENSIONS
• The dimensions of a matrix with m rows and n
columns are m X n.
2
3
−1 8
0 1.2
• The matrix has 3 rows and 2 columns so the
dimensions are 3 X 2.
ELEMENTS
• The numbers in a matrix are its elements.
2
3
−1 8
0 1.2
• Elements are identified by their row and column.
Thus, element 3,2 is 1.2.
EQUAL MATRICES
• Equal matrices have the same dimensions and the
elements in corresponding positions are equal.
SCALAR MULTIPLICATION
• In matrix algebra, a real number is often called a
scalar. To perform scalar multiplication, you multiply
each element in the matrix by the scalar.
PROPERTIES OF MATRICES
• Associative Property of Addition
o(A + B) + C = A + (B + C)
• Commutative Property of Addition
oA + B = B + A
oWe will see tomorrow that matrices do not
have the commutative property of
multiplication
• Distributive Property of Addition/Subtraction
ok(A + B) = kA + kB
ok(A – B) = kA – kB
ADDING AND SUBTRACTING MATRICES
• To add or subtract two matrices, simply add or
subtract corresponding elements.
• You can add or subtract matrices only if they have
the same dimensions.
TRY THIS!
• Perform the indicated operation, if possible.
6
1
−2 3
3 2
−2
0
7
1
1
3 + −2
6
1
−4
9
5
TRY THIS!
• Perform the indicated operations, if possible.
0
3 −7
6
2
−1
4
1
−2
3
0
−5
MULTI-STEP PROBLEM
• Two pet stores sell both dogs and cats. Sales from
each store for last month and this month are shown
below:
• Organize the data into matrices, then write and
interpret a matrix giving the average monthly sales
for the two month period.
• Last Month: Store 1 sold 42 dogs, 33 cats. Store 2 sold 56
dogs, 21 cats.
• This Month: Store 1 sold 36 dogs, 51 cats. Store 2 sold 48
dogs, 37 cats.
ONE MORE!
• Solve the matrix equation for x and y.
−2
1
3 −2𝑥
−
−5𝑦
1
7
−6
−4
=
4
8
12
−6
ON YOUR CALCULATOR
• Let’s see how to input matrices in the calculator