Find the inverse of the matrix using elementary matrices. [[2,0],[1,1]]

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Find the inverse of the matrix using elementary matrices. [[2,0],[1,1]]

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asked 2021-02-08

Use elementary matrices to write ? in row reduced echelon form. Use the elementary matrices to find the inverse of
\(A=\begin{bmatrix}1 & 0&-2 \\0& 2&1\\0&0&1 \end{bmatrix}\)

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asked 2020-11-08

Which of the following matrices is elementary matrix?
a) \(\begin{bmatrix}0 & 3 \\1 & 0 \end{bmatrix}\)
b) \(\begin{bmatrix}2 & 0 \\0 & 1 \end{bmatrix}\)
c) \(\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix}\)
d) \(\begin{bmatrix}2 & 0 \\0 & 2 \end{bmatrix}\)

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asked 2020-12-07

Let \(A=\begin{bmatrix}1 & 2 \\-1 & 1 \end{bmatrix} \text{ and } C=\begin{bmatrix}-1 & 1 \\2 & 1 \end{bmatrix}\)
a)Find elementary matrices \(E_1 \text{ and } E_2\) such that \(C=E_2E_1A\)
b)Show that is no elementary matrix E such that C=EA

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asked 2021-01-22

Given the matrix
\(A=\begin{bmatrix}0 & 0&1 \\ 0 & 3&0 \\ 1&0 & -10 \end{bmatrix}\)
and suppose that we have the following row reduction to its PREF B
\(A=\begin{bmatrix}0 & 0&1 \\ 0 & 3&0 \\ 1&0 & -10 \end{bmatrix}\Rightarrow\begin{bmatrix}1 & 0&-10 \\ 0 & 3&0 \\ 0&0 & 1 \end{bmatrix}\Rightarrow\begin{bmatrix}1 & 0&-10 \\ 0 & 1&0 \\ 0&0 & 1 \end{bmatrix}\Rightarrow\begin{bmatrix}1 & 0&0 \\ 0 & 1&0 \\ 0&0 & 1 \end{bmatrix}\)
Write \(A \text{ and } A^{-1}\) as product of elementary matrices.

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asked 2021-03-07

Can you please help with finding an inverse of an elementary matrices?

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asked 2021-01-30

Given the matrices
\(A=\begin{bmatrix}5 & 3 \\ -3 & -1 \\ -2 & -5 \end{bmatrix} \text{ and } B=\begin{bmatrix}0 & -2 \\ 1 & 3 \\ 4 & -3 \end{bmatrix}\)
find the 3x2 matrix X that is a solution of the equation. 2X-A=X+B
X=?

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asked 2021-02-02

Given the matrices
\(A=\begin{bmatrix}-1 & 3 \\2 & -1 \\ 3&1 \end{bmatrix} \text{ and } B=\begin{bmatrix}0 & -2 \\1 & 3 \\ 4 & -3 \end{bmatrix}\) find the \(3 \times 2\) matrix X that is a solution of the equation. 8X+A=B

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asked 2021-03-02

Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA.
\(A=\begin{bmatrix}3 & -2 \\1 & 5\end{bmatrix} , B=\begin{bmatrix}0 & 0 \\5 & -6 \end{bmatrix}\)

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asked 2021-02-14

Let \(A=\begin{bmatrix}1 & 2&-1 \\1&0&3\\1&1&-1 \end{bmatrix}\)
i) Find the determinant of A
ii)Verify that the matrix
\(\begin{bmatrix}-\frac{3}{4} & \frac{1}{4}&\frac{6}{4} \\1&0&-1\\\frac{1}{4}&\frac{1}{4}&-\frac{1}{2} \end{bmatrix}\) is the inverse matrix of A

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asked 2020-11-17

Let \(A=\begin{pmatrix}2 &1 \\6 & 4 \end{pmatrix}\)
a) Express \(A^{-1}\) as a product of elementary matrices
b) Express A as a product of elementary matrices

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Answer 1

Let the given matrix be,
\(A=[[2,0],[1,1]]\)
Now transform the given matrix in to unit matrix I by performing column reduction to get,
\(A=[[2,0],[1,1]]\)
\(=[[2,0],[1,1]](c_1 -> c_1 - c_2)\)
\(=[[1,0],[0,1]](c_1 -> 1/2 * c_1)\)
=I
Now, construct sequence of elementary matrices such that E2*E1 A=I
The column operation are,
\(E_1=[[1,0],[0,1]](c_1 -> c_1 - c_2)\)
\(=[[1,0],[-1,1]]\)
\(E_2=[[1,0],[0,1]](c_1 -> 1/2 * c_1)\)
\(=[[1/2,0],[0,1]]\)
Then the inverse of the matrix by elementary matrices is given by:
\(A^(-1)=E_1xxE_2\)
\(=[[1,0],[-1,1]]*[[1/2,0],[0,1]]\)
\(=[[1/2,0],[-1/2,1]]\)

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Find the inverse of the matrix using elementary matrices. [[2,0],[1,1]]

Find the inverse of the matrix using elementary matrices. [[2,0],[1,1]]

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