Matrices Vocabulary PreCal/TRIG Fall 2021
Reduced Row Echelon Form
1. All leading coefficients are 1. 2. Any element ABOVE or BELOW a leading coefficient is 0. 3. The leading coefficient of any row is always to the left of the leading coefficient of the row below it. 4. All rows containing all 0s are at the bottom of the matrix.
Row Echelon Form
1. Each leading entry in a row is 1. 2. If a column contains a leading entry, then all of the elements BELOW the leading entry are ZERO 3. In any two consecutive (non-zero) rows, the leading entry in the upper row occurs to the left of the lower row. 4. All rows consisting entirely of zeros appear at the bottom of the matrix.
What are the 3 Elementary Row Operations?
1. switch any 2 rows 2. Multiply any row by a non-zero constant 3. Add one row to another
The only way that 2 matrices can be added.
Both must be of the same dimension (they must have the same number of rows and columns)
True/False: Matrix multiplication is commutative
False
Dimensions of a Matrix
It describes the SIZE of a matrix. The first number is the number of rows and the second number is the number of columns.
scalar multiplication
Multiplying a matrix by a number. This will multiply EVERY element in the matrix by that number.
The way to write "switch row 3 with row 4"
R3 ⟷ R4
adjugate of a 2 x 2 matrix
Switch the places of a and d, change the signs of b anc c in your matrix to get this
additive inverse
The matrix obtained by changing the sign of every matrix element.
True/False: Matrix addition is commutative
True
adding and subtracting matrices
Two matrices of the same order can be added or subtracted, by adding or subtracting corresponding elements.
additive identity matrix
a matrix filled with all zeros.
augmented matrix
a matrix of numbers in which each row represents the constants from one equation, and each column represents all the coefficients for a single variable.
matrix multipliction
a process of multiplying rows by columns. To multiply a row matrix by a column matrix, each element in the row matrix is multiplied by each element in the column matrix and the results added.
matrix
a rectangular array of numbers or symbols (elements) enclosed in brackets
identity matrix
a square matrix in which the diagonal elements are 1s and the remaining elements are zeroes.
How a Matrix is named
by a capital letter
Entry
each value in a matrix -- it is described by it's location
scalar
having magnitude - not direction (A NUMBER VALUE - 1, 3/4, and 0.24 could be scalars)
transpose
is obtained by interchanging the rows and columns of a matrix
square matrices
number of rows = number of columns
column matrices
only have 1 column
row matrices
only have 1 row
multiply by the inverse
since we can't divide by a matrix we instead do this
multiplicative inverse matrix
the matrix that gives you the identity matrix when multiplied by the original matrix.