CHAPTER 12 ALG2

When are two matrices​ equal?

Each entry in each row and column position are the same

To find the product AB of two matrices A and​ B, which of the following must be​ true?

The number of columns in A must equal the number of rows in B.

Which of the following is NOT a property of matrix​ multiplication?

To multiply​ matrices, multiply corresponding entries.

If AXequals=B represents a matrix equation where A is a nonsingular​ matrix, then we can solve the equation using Xequals=​__________.

a-1b

The matrix used to represent a system of linear equations is called​ a(n) __________ matrix.

augmented

If a system of equations has one​ solution, the system is ____________, and the equations are _______

consistent and dependent

If the lines that make up a system of two linear equations are​ coincident, the system is​ __________ and the equations are​ __________.

consistent and dependent

cramer rule what is the fraction

d of x over d

If A and B are square​ matrices, then ABequals=BA.

false

If any row​ (or any​ column) of a determinant is multiplied by a nonzero number​ k, the value of the determinant remains unchanged.

false

If a system of equations has no​ solution, it is said to be

inconsistent

Suppose that A is a square n by n matrix that is nonsingular. The matrix B such that AB equals BA equals Upper I Subscript nAB=BA=In is called the​ _______ of the matrix A.

inverse matrix

An m by n rectangular array of numbers is called​ a(n)

matrix

If a system of two linear equations in two variables is​ inconsistent, which of the following best describes the graphs of the lines in the​ system?

parallel

The notation a 35a35 refers to the entry in the​ _______ row and​ _______ column of a matrix.

row three and column 5

If a matrix A has no​ inverse, it is called a​ __________.

singular matrix

A matrix that has the same number of rows and columns is called​ a(n) _______ matrix.

square matrix

If any two rows of a determinant are​ interchanged, its value is best described by which of the​ following?

the determinant changes signs

Matrix addition is commutative.

true

The identity matrix has properties similar to those of the real number 1.

true

can the determinant be 0

yes

row echelon form

zeros below the 1s

reduced row echelon form

zeros except for the 1s