High School
SAT
ACT
University
MCAT
LSAT
DAT

Matrix Inversion Algorithm

Related Topics

Wize University Linear Algebra Textbook > Matrices

Matrix Inverse Algorithm

4 Activities

checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.

Example: Matrix Inverse Algorithm

Find the inverse of A=[1325]A=\left[\begin{array}{rr}1 & 3\\2 & 5\end{array}\right] using the formula for a 2×22\times2 matrix, and using the Gauss-Jordan elimination algorithm.
More Matrix Inverse Algorithm Questions:
Practice: Method of Inverse
Practice Question: Method of Inverse
Given the matrix A=[2130101−12]A=\left[\begin{array}{rrr} 2&1&3\\ 0&1&0\\ 1&-1&2 \end{array}\right],
Practice: Method of Inverse
Practice Question: Method of Inverse
Given the matrix A=[2130101−12]A=\left[\begin{array}{rrr} 2&1&3\\ 0&1&0\\ 1&-1&2 \end{array}\right],
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
133 - FML 3 - 18.1W e.g. 10
Find the value(s) of c such that A is NOT invertible given A=  [c−c1−1−1−11−cc]\bcb{\boldsymbol{ A =  \begin{bmatrix} c & -c & 1 \\ -1 & -1 & -1 \\ 1 & -c & c \end{bmatrix} }}
Practice: Matrix Inverse
Find all values of k so that the matrix [−2003102−1k]\begin{bmatrix} -2&0&0\\ 3&1&0\\ 2&-1&k \end{bmatrix} has an inverse.
Find the inverse of A=[101011110]A=\begin{bmatrix} 1&0&1\\ 0&1&1\\1&1&0 \end{bmatrix} .
For each of the following matrices, find the inverse or state why the inverse does not exist.
A=[1−1−2100012]A=\begin{bmatrix} 1&-1&-2\\ 1&0&0\\ 0&1&2 \end{bmatrix}
B=[3191506]B=\begin{bmatrix} 3&1&9\\ 15&0&6 \end{bmatrix}
Practice: Matrix Inverse
Find all values of k for which the matrix [2−6−1k2−22]\begin{bmatrix} 2&-6\\ -1&k^2-22 \end{bmatrix} has no inverse.
Practice: Matrix Inverse
Find the inverse of the following matrices:
a.) A=[4534]A=\begin{bmatrix} 4&5\\ 3&4 \end{bmatrix}
b.) B=[−1−2024113−2]B=\begin{bmatrix} -1&-2&0\\ 2&4&1\\ 1&3&-2 \end{bmatrix}
Matrix Inverse
Practice: Matrix Inverse
If [1ax2by0cz]\left[\begin{array}{c} 1&a&x\\ 2&b&y\\ 0&c&z \end{array}\right] is the inverse of the matrix[1p0−3q42r1]\left[\begin{array}{c} 1&p&0\\ -3&q&4\\ 2&r&1 \end{array}\right], find the value of rr.
Let A=[214103421]A=\begin{bmatrix}2&1&4\\1&0&3\\4&2&1\end{bmatrix}. Find A−1A^{-1} if possible.
Find the inverse of [021255121]\begin{bmatrix} 0 &2& 1\\ 2 &5 &5\\ 1 &2 &1 \end{bmatrix}
The following matrix A depends on a parameter p. Find all the values of the parameter p for which the
corresponding matrix is not invertible.
A=[123410002000300040010𝑝𝑝+1𝑝+20−𝑝−2𝑝+1−3𝑝+2]A=\begin{bmatrix} 1&2&3&4\\ 1000&2000&3000&4001\\ 0&𝑝&𝑝 + 1&𝑝 + 2\\ 0&−𝑝&−2𝑝 + 1&−3𝑝 + 2 \end{bmatrix}
For what value or values of a (if any) is the matrix below invertible?
[1210350𝑎1]\begin{bmatrix} 1& 2& 1\\ 0 &3& 5\\ 0 &𝑎 &1 \end{bmatrix}
The following matrix A depends on a parameter p. Find all the values of the parameter
p for which the corresponding matrix is not invertible.
A=[123410002000300040010𝑝𝑝+1𝑝+20−𝑝−2𝑝+1−3𝑝+2]A=\begin{bmatrix} 1&2&3&4\\ 1000&2000&3000&4001\\ 0&𝑝&𝑝 + 1&𝑝 + 2\\ 0&−𝑝&−2𝑝 + 1&−3𝑝 + 2 \end{bmatrix}
Practice Question 3: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Find all the values of k for which the matrix A has an inverse
A=[210102102k]A=\begin{bmatrix} 2&1&0\\ 1&0&2\\ 1&0&2k \end{bmatrix}
Practice: Method of Inverse
Practice Question: Method of Inverse
Given the matrix A=[2130101−12]A=\left[\begin{array}{rrr} 2&1&3\\ 0&1&0\\ 1&-1&2 \end{array}\right],
Find all the values of 𝑘 such that the matrix 𝐴=[33−610−k2]has an inverse.\text{Find all the values of 𝑘 such that the matrix 𝐴}=\begin{bmatrix} 3&3\\ -6&10-k^2 \end{bmatrix}\text{has an inverse.}
Matrix Inverse
If [1ax2by0cz]\left[\begin{array}{c} 1&a&x\\ 2&b&y\\ 0&c&z \end{array}\right] is the inverse of the matrix[1p0−3q42r1]\left[\begin{array}{c} 1&p&0\\ -3&q&4\\ 2&r&1 \end{array}\right], find the value of rr.
Practice: Adjoint Matrix
Let B=[1−102111000−11−21−2−1]B=\left[\begin{array}{rrrr} 1&-1&0&2\\ 1&1&1&0\\ 0&0&-1&1\\ -2&1&-2&-1 \end{array}\right], and note that det(B)=−1\text{det}(B)=-1
Use the determinant and the adjoint of BB to find the entry in position (4,3)(4,3) of the matrix B−1B^{-1}
Find the inverse of the matrix [10221−13−215]\begin{bmatrix} 1&0&2\\ 2&1&-1\\ 3&-2&15 \end{bmatrix}.
Find the inverse of the matrix A=[10221−13−215]A=\left[\begin{array}{rrr} 1&0&2\\ 2&1&-1\\ 3&-2&15 \end{array}\right]
Matrix operations
Suppose that A=[1−103−20041]A=\begin{bmatrix}1 & -1 & 0\\3 & -2 & 0\\0 & 4 & 1\end{bmatrix}and BBis a 3×23 \times 2matrix. If the product AB=[34011−2]AB = \begin{bmatrix}3 & 4\\0 & 1\\1 & -2\end{bmatrix}, find the (1,2)-entry of BB(i.e. B12B_{12}).
Invertible matrix
For what value(s) of aawill the matrix [2−43a]\begin{bmatrix}2 & -4\\3 & a\end{bmatrix} be invertible?
Matrix Inverse
Practice: Matrix Inverse
If [1ax2by0cz]\left[\begin{array}{c} 1&a&x\\ 2&b&y\\ 0&c&z \end{array}\right] is the inverse of the matrix[1p0−3q42r1]\left[\begin{array}{c} 1&p&0\\ -3&q&4\\ 2&r&1 \end{array}\right], find the value of rr.
Practice Question: Matrix Inverse
Practice Question: Matrix Inverse
If [1ax2by0cz]\left[\begin{array}{} 1&a&x\\ 2&b&y\\ 0&c&z \end{array}\right] is the inverse of the matrix[1p0−3q42r1]\left[\begin{array}{} 1&p&0\\ -3&q&4\\ 2&r&1 \end{array}\right], find the value of rr.
Suppose that A=[1−1031−4]A=\begin{bmatrix}1 &-1&0\\3&1&-4\end{bmatrix} and RRis the reduced row echelon form of AA. Find the invertible matrix UUsuch that R=UAR=UA.
For what value(s) of aawill the matrix [2−43a]\begin{bmatrix}2 & -4\\3 & a\end{bmatrix}be invertible?
Practice: Matrix Inverse
Find all values of k for which the matrix [2−6−1k2−22]\begin{bmatrix} 2&-6\\ -1&k^2-22 \end{bmatrix} has no inverse.
Practice: Matrix Inverse
Practice Question: Matrix Inverse
Find all the values of kk such that the matrix[210102102k]\begin{bmatrix} 2&1&0\\ 1&0&2\\ 1&0&2k \end{bmatrix} has an inverse.
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of kk will the matrix[1210150k1]\left[\begin{array}{rrr} 1&2&1\\ 0&1&5\\ 0&k&1 \end{array}\right] be invertible?
Practice Question 1: Matrix Inverse
Practice Question: Matrix Inverse
Find all the values of kk such that the matrix[210102102k]\begin{bmatrix} 2&1&0\\ 1&0&2\\ 1&0&2k \end{bmatrix} has an inverse.
Practice: Matrix Inverse
Find all values of k so that the matrix [−2003102−1k]\begin{bmatrix} -2&0&0\\ 3&1&0\\ 2&-1&k \end{bmatrix} has an inverse.
Practice: Matrix Inverse (~2016 Test2 #15)
Practice: Matrix Inverse
Find all the values of kk such that the matrix[210102102k]\begin{bmatrix} 2&1&0\\ 1&0&2\\ 1&0&2k \end{bmatrix} has an inverse.