matrices Flashcards
column
line of numbers vertically
row
line of numbers vertically
element
each number or variable of a matrix
how do you name a matrix
row number then column number
column matrix
matrix with one column
trace
sum of numbers of the leading diagonal in a matrix
square matrix
matrix with same number of rows and columns
row matrix
matrix with one row
diagonal matrix
only has non zero values along the leading diagonal
unit matrix
only has non zero values along the leading diagonal and that value is a one
upper triangular matrix
only has non zero values along leading diagonal and above
lower triangular matrix
only has non zero values below the leading diagonal
transpose
turn rows into columns and columns into rows
how do you do addition with matrices
add each element in the matrices
do matrices that you are adding need to have the same number of elements
yes
how do you do subtraction with matrices
subtract each element in the matrix with the minus sign from the other matrix
how do you multiply matrices
go through each row in the column matrix and multiply by the rows in the other matrix (see video for more information)
does the number of columns in the first matrix have to be equal to the number of rows in the second matrix when multiplying
yes
how do you find the size of the matrix after multiplication
number of rows in first matrix and number of columns in the second matrix (see lecture for how to multiply matrices)
determinant
written with modulus sign is a scalar value found by multiplying the values on the leading diagonal together and then subtracting the result of the multiplication of the numbers in the other diagonal
minor
removing rows and columns to make finding a determinant possible
how are the signs found when finding a determinant in a matrix
the signs alternate
how do you find the inverse of a matrix
- find determinant
- create matrix of minors by replacing each element with the determinant found when it is a minor
- create the matrix of cofactors by alternating plus and minus signs in the matrix
- find adjoint by transposing the matrix of cofactors
- divide adjoint by determinant
how to divide matrices
multiply the matrix you are dividing with the inverse of the other matrix
