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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: Unknown 1989;
Typology: Study notes
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Matrix Arithmetic on the TI-
The size (dimension) of a matrix is always given in terms of its number of rows and number of columns.
A 2 x 4 matrix has 2 rows and 4 columns. Square matrices have the same number of rows and columns.
Only matrices of the same size can be added or subtracted.
has 1s on the main diagonal (running from upper left to lower right) and 0s elsewhere.
Some square matrices have inverses. If A โ1^ and A are inverse matrices , then A โ1A = A A โ 1^ equals
Any matrix may be multiplied by any real number (called a scalar ). Each element of the matrix is
multiplied by the scalar.
Two matrices can be multiplied if and only if the number of columns in the first matrix is the same as the number of rows in the second. Any square matrix can be raised to a power.
A zero matrix 0 may be of any size and has 0s as all of its elements.
Entering a Matrix
To enter a 2 x 3 matrix as matrix A: MATRIX EDIT NAMES 1:[A] ENTER MATRIX[A] 2 ENTER 3 ENTER 1 ENTER 2 ENTER 4 ENTER 1 ENTER 0 ENTER - ENTER 2nd QUIT
Displaying a Matrix
Adding or Subtracting Matrices
MATRIX NAMES 1:[A] ENTER + MATRIX NAMES 2:[B] ENTER ENTER
Multiplying a Matrix by a Scalar
Multiplying Matrices
MATRIX NAMES 1:[A] ENTER x MATRIX NAMES 2:[B] ENTER ENTER
Raising a Matrix to a Power
Entering an Identity Matrix
One way to enter an identity matrix is to simply enter the required elements as you would any other matrix. A shortcut for entering the 3 x 3 identity matrix is: MATRIX MATH 5:identity( ENTER
3 ) STO+ MATRIX NAMES 4:[D] ENTER.
Examples of Matrix Calculations
Enter these matrices: A = 3 โ 5 , B = , C = , D = , 0 0
E = โ 4^6 , F = , and G =
Addition of matrices is commutative, i.e. A + B = B + A.
Subtraction of matrices is not commutative, i.e. A - B ร B - A.
A + F does not exist because the matrices do not have the same size.
Scalar multiplication of a matrix is commutative, i.e. k A = A k.
Scalar multiplication is distributive over matrix addition, i.e. k( B + E ) = k B + k E. Scalar multiplication is also distributive over matrix subtraction.
The product of a square matrix and the identity matrix [of the same order] is the original matrix. Such multiplication is commutative, i.e. CI = IC.
Multiplication of matrices is not commutative, i.e. AB ร BA.
The product of two matrices may be 0 , even if neither matrix is 0!
CF does not exist because the number of columns in C is not the same as the number of rows in F. The size of the product of two matrices [assuming the product exists] is the number of rows in the first matrix by the number of columns in the second.
The square of a nonzero matrix may be 0.
G โ 1^ = __________ [convert to fractions by using MATH 1 ]