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Level 419

Matrices & Determinants


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matrix
a rectangular array of elements (or entries) set out by rows and columns
elements
What are the objects in a set called?
rows
what does the 2 represent in 2x3
columns
what does the 3 represent in 2x3
dimensions
the rows by columns of a matrix
row matrix
a matrix has only 1 row
column matrix
a matrix has only 1 column
square matrix
the same number of elements in the rows and columns.
zero matrix
matrix containing zeros
equal matrices
-dimensions are the same
identity matrix
diagonal matrix with ones in the leading diagonal and zeros in the other positions.
scalar
A term used in matrix multiplication to describe a real number as opposed to a matrix
matrix multiplication
-can be multiplied if the # of A columns = # of B rows
8
[1 4] solve for det A
determinant
ad-bc; must be nonzero for an invertible matrix
2 X 2 determinant
the ad elements - the bc elements
-2
solve det A for the matrix [1 2]
3 X 3 determinant
diag 1+ diag 2 + diag 3- (across 1-across 2-across 3)
no solution: determinant ≠ 0
evaluate det B: for [ 0 0]
undefined determinant
determinant = 0
diagonal matrix
has zeros in all positions other than the leading diagonal which contains numbers other than zero.
inverse of matrix
the inverse of A, or A to the -1 power
x matrix
x values of matrix
constant matrix
constant numbers in a matrix
coefficient matrix
A matrix used to solve a system of linear equations with Cramer's rule, in which the elements of the matrices are the coefficients of the variables
Cramer's rule
A formula for solving a system of two linear equations using matrices