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*
  • A^T
  • A^-1 (correct)
  • A'

    • 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?

    <p>It is singular</p> Signup and view all the answers

    How many inverses can a matrix have?

    <p>Exactly one</p> Signup and view all the answers

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

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

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

    <p>When A is invertible</p> Signup and view all the answers

    What does I1 n = In denote?

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

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

    <p>The row vectors form a basis for Rn</p> Signup and view all the answers

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

    <p>Invertible</p> Signup and view all the answers

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