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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.
There are an infinite number of special square matrices called identity matrices. An identity matrix I
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
the identity matrix I , of the appropriate size.
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
MATRIX NAMES 1:[A] ENTER ENTER
Adding or Subtracting Matrices
MATRIX NAMES 1:[A] ENTER + MATRIX NAMES 2:[B] ENTER ENTER
Multiplying a Matrix by a Scalar
3 MATRIX NAMES 1:[A] ENTER ENTER
Multiplying Matrices
MATRIX NAMES 1:[A] ENTER x MATRIX NAMES 2:[B] ENTER ENTER
Raising a Matrix to a Power
MATRIX NAMES 2:[B] ENTER ^ 3 ENTER
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 =
A + B = __________ B + A = __________
Addition of matrices is commutative, i.e. A + B = B + A.
A โ B = __________ B โ 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.
2 A = __________ A * 2 = __________
Scalar multiplication of a matrix is commutative, i.e. k A = A k.
5( B + E ) = __________ 5 B + 5 E = __________
Scalar multiplication is distributive over matrix addition, i.e. k( B + E ) = k B + k E. Scalar multiplication is also distributive over matrix subtraction.
CI = __________ IC = __________
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.
AB =___________ BA = __________
Multiplication of matrices is not commutative, i.e. AB ร BA.
BE = __________
The product of two matrices may be 0 , even if neither matrix is 0!
FC = __________
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.
A 2 = AA = _______ B 2 = _______
The square of a nonzero matrix may be 0.
G โ 1^ = __________ [convert to fractions by using MATH 1 ]
