Algebra II ch. 4 test

Matrix

an array of numbers arranged in rows and columns

Any two matrices can be multiplied together.

false

If a system of equations is dependent, then it does not have a solution.

false

If matrices A and B are inverse of each other, then AI=B and BI=A.

false

Matrix multiplication is commutative.

false

Dependent

infinitely many solutions

Inconsistent

no solution

Dimensions of a matrix

numbers of rows X number of columns

Independent

only 1 solution

If the calculator says Error...

that means the matrix would not have an inverse because the det would be 0 and if the det is 0 it can't have an inverse

If a matrix has A dimensions mXn and matrix B has dimensions nXr, then...

the product AB has dimensions mXr

If you multiply a 1X3 matrix and a 3X1 matrix...

the product is a 1X1 matrix

A is a square matrix with n rows and n columns. If there is an nXn matrix B such that AB=I and BA=I...

then A and B are inverse of one another

A is a square matrix with n rows and n columns. I is a matrix with the same dimensions and with ones on the main diagonals and zeros elsewhere.

then AI=IA=A

Two matrices are equal if they have the same dimensions and the corresponding entries are equivalent.

true

When adding or subtracting matrices, their dimensions must be the same.

true

No solution

when there is 0001 in the bottom row of an augmented matrix

Infinitely many solution

when there is a row of zeros in the bottom row of an augmented matrix