Exercise · ZW-INVERSE-MATRIX-001 · ★☆☆ Basic
Compute the inverse of \(\begin{pmatrix}2 & 1 \\ 5 & 3\end{pmatrix}\).
Choose one option.
Show answer
- B. \(\begin{pmatrix}3 & -1 \\ -5 & 2\end{pmatrix}\)
Explanation
With \(ad-bc=1\), the inverse is \(\frac{1}{ad-bc}\begin{pmatrix}d & -b\\ -c & a\end{pmatrix}\): swap the diagonal entries and change the sign of the other two. Check that \(AA^{-1}=I\).
Review the concept: Inverse matrix
The inverse of a square matrix \(A\) is the matrix \(A^{-1}\) that gives the identity \(I\) when multiplied by \(A\) on either side; if it exists, \(A\) is called invertible.
\[AA^{-1}=A^{-1}A=I\]
More practice problems: inverse matrix
- ZW-INVERSE-MATRIX-002 Which of these matrices has NO inverse?
- ZW-INVERSE-MATRIX-003 Compute the inverse of the diagonal matrix [2 0 0; 0 -4 0; 0 0 5].
- ZW-INVERSE-MATRIX-004 If A and B are invertible matrices of the same size, what is (AB)^-1?
- ZW-INVERSE-MATRIX-005 Solve Ax=b using the inverse, with A=[1 2; 3 5] and b=(1,2)^T.
- ZW-INVERSE-MATRIX-006 A square matrix A satisfies A^2-3A+I=0. Which expression is A^-1?
- ZW-INVERSE-MATRIX-007 Let A=[1 2 0; 0 1 3; 0 0 1]. What is the entry in row 1, column 3 of A^-1?
- ZW-INVERSE-MATRIX-008 If A is an invertible 2×2 matrix, what is (3A)^-1?
- ZW-INVERSE-MATRIX-009 Select all values of k for which [k 2; 8 k] is NOT invertible.