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Material Type: Notes; Class: MATH 1630: If high school precalculus and ACT math of at least 21 contact 694-6450.; Subject: Mathematics; University: Pellissippi State Technical Community College; Term: Fall 2006;
Typology: Study notes
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Matrix Arithmetic ~ page 1
Addition and Subtraction of Matrices
a. In a square matrix m = n b. In a row matrix m = 1 c. In a column matrix n = 1
equal.
a. Given that:
9 7 m 3 n 5
r 0 8 0
b. Then: 9 = m - 3 | m = 12 7 = n + 5 | n = 2 r = 8
cannot add or subtract matrices if they are not the same size.
and is denoted by - X.
is one to match a matrix of any size.
The 0 matrix of order 2 x 4 is
Matrix Arithmetic ~ page 2
Scalar Multiplication
If A = , then 3 A = 3 =
Matrix Multiplication
a. It is not always possible to multiple two given matrices, even if they are the same size. b. It may be possible to multiply A times B (in that order), but not B times A. c. It may be possible to multiply A times B and B times A , but not get the same answer!
a. Suppose that we have matrix A which is 3x2 and matrix B which is 2x3. b. Write the orders of the matrices side-by-side and compare the two “inner” numbers c. If the number of columns in the first matrix is equal to the number of rows in the second matrix, then the product AB can be found. d. If the product exists, then its size is given by the two “outer” numbers.
matrix matrix 3 x 2 2 x 3
must be will be 3 x 3
e. Would we be able to find BA in this case? Yes, it will be a 2x2 matrix.
matrix matrix 2 x 3 3 x 2
must be will be 2 x 2
that the “real” numbers do.