10 Questions
What is an n ⇥ n matrix B called if AB = BA = In?
Nonsingular
How is the inverse of a matrix A denoted?
A^-1
Which statement is equivalent to the invertibility of a matrix A?
det(A) 6= 0
What happens if a matrix has no inverse?
It is singular
How many inverses can a matrix have?
Exactly one
What does (AT )1 = (A1)T represent?
(AT )1 is the transpose of A and (A1)T is the inverse of A
When can Ax = b be consistent for every n ⇥ 1 matrix b?
When A is invertible
What does I1 n = In denote?
(I1)n is the identity matrix and In is the inverse of I
What does it mean when the row vectors of a matrix are linearly independent?
The row vectors form a basis for Rn
What is a matrix called if it is row equivalent to the identity matrix In?
Invertible
This quiz covers the definition of matrix inverses, including the conditions for a matrix to have an inverse, properties of nonsingular matrices, and the process of finding the inverse of a matrix. It also discusses the notation for denoting the inverse of a matrix.
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