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Matrix Inverses: Definition and Theorems

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Matrix Inverses: Definition and Theorems

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Questions and Answers

What is an n ⇥ n matrix B called if AB = BA = In?

Singular

Identity

Trivial

Nonsingular (correct)

How is the inverse of a matrix A denoted?

A^T

A^-1 (correct)

Which statement is equivalent to the invertibility of a matrix A?

The reduced echelon form of A is In

Ax = 0 has only the trivial solution

det(A) 6= 0 (correct)

The column vectors of A span Rn

What happens if a matrix has no inverse?

It is singular Signup and view all the answers

How many inverses can a matrix have?

Exactly one Signup and view all the answers

What does (AT )1 = (A1)T represent?

(AT )1 is the transpose of A and (A1)T is the inverse of A Signup and view all the answers

When can Ax = b be consistent for every n ⇥ 1 matrix b?

When A is invertible Signup and view all the answers

What does I1 n = In denote?

(I1)n is the identity matrix and In is the inverse of I Signup and view all the answers

What does it mean when the row vectors of a matrix are linearly independent?

The row vectors form a basis for Rn Signup and view all the answers

What is a matrix called if it is row equivalent to the identity matrix In?

Invertible Signup and view all the answers