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chapter 4 terms
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Gravity
Terms in this set (37)
matrix
mold used in the production of phonograph records, type, or other relief surface
matrix element
every item listed in a matrix is an element of the matrix. an element is identified by it's position in the matrix.
matrix addition
the addition of matrices
zero matrix
a matrix in which every element is zero
matrix subtraction
A - B = A + (-B)
matrix equation
An equation in which the variable is a matrix.
equal matrix
A matrix with the same dimensions and equal corresponding elements
5 properties chart
a chart displaying the 5 properties
scalar
a variable quantity that cannot be resolved into components
scalar product
a real number (a scalar) that is the product of two vectors
scalar multiplication
the multiplication of each entry in a matrix by the same number
matrix multiplication
the multiplication of matrices
dimensions of a product matrix
If matrix a is an m X n matrix and matrix B is an n X p matrix, then the product matris AB is an m X p matrix.
4 properties of matrix multiplication
the four properties of matrix multiplication
transformation
the act of changing in form or shape or appearance
image
the altered figure in a translation.
preimage
The original figure in a transformation.
translation
the act of changing in form or shape or appearance
dilation
A transformation that changes the size of an object, but not the shape.
reflection
a likeness in which left and right are reversed
rotation
a transformation in which the coordinate axes are rotated by a fixed angle about the origin
center of rotation
the point about which a figure is rotated
matrices for rotation in coordinate plane
the points where a plane comes to a rotation
square matrix
a matrix with the same number of rows and columns
multiplicative identity matrix
a square matrix with 1 in every entry of the main diagonal and 0 in every other entry
multiplicative inverse of a matrix
If A and X are N x N matricies an AX= XA = I, then X is the multiplicative inverse
determinant of a 2x2 matrix
multiply numbers on primary diagonal - multiplied numbers on secondary diagonal
inverse of a 2x2 matrix
I = (A) x (A⁻¹) matrix x inverse = identity matrix
determinant of a 3x3 matrix
1. rewrite first two columns outside of matrix on right
2. multiply each trio of numbers on each diagonal
3. add first three products from diagonals together and subtract second three products from diagonals
evaluating the determinant of a 3x3 matrix
1.verify that A and B are inverses by showing: BA=I
2.verify that C and D are not inverses by showing that DC = I
finite graph
a graph where the 3x3 matrix is used
coefficient matrix
a matrix whose entries are the coefficients of each variable in a system
variable matrix
matrix containing the variables of the system
constant matrix
matrix containing the constants of the system
cramer's rule
a method of solving systems of linear equations by using determinants
augmented matrix
a coefficient matrix with an extra column containing the constant terms
row operations
To solve a system of equations using an augmented matrix you can use one or more of the following row operations:
1. switch any two rows
2. multiply a row by a constant
3. add one row to another
4. Combine one or more of these steps
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