The matrix A=[-2 2 1 3 ] is invertible with A^(-1)=1/8 [-3 2 1 2 ].$A$ be a $2times 2$ real matrix with trace $2$ and determinant $-3$Intuition behind Matrix being invertible iff determinant is non-zeroFor what values of x,the following matrix is invertibleInverting a $3times 3$ block matrixHow to prove that If A is invertible then $A^-1$ and $A^2$ are invertible.Does every invertible matrix A has a matrix B such that A=Adj(B)?Determine the Value of C of the matrix which Matrix A is not invertibleInvertible matrix and eigenvalueInvertible matrix and spanSimilar matrices with same invertible matrix.
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The matrix A=[-2 2 1 3 ] is invertible with A^(-1)=1/8 [-3 2 1 2 ].
$A$ be a $2times 2$ real matrix with trace $2$ and determinant $-3$Intuition behind Matrix being invertible iff determinant is non-zeroFor what values of x,the following matrix is invertibleInverting a $3times 3$ block matrixHow to prove that If A is invertible then $A^-1$ and $A^2$ are invertible.Does every invertible matrix A has a matrix B such that A=Adj(B)?Determine the Value of C of the matrix which Matrix A is not invertibleInvertible matrix and eigenvalueInvertible matrix and spanSimilar matrices with same invertible matrix.
$begingroup$
The matrix $A=beginpmatrix -2 & 2 \ 1 & 3 endpmatrix$ is invertible with $A^-1=frac18 beginpmatrix-3 & 2\ 1 & 2 endpmatrix$.
(TRUE/FALSE)? In my opinion the answer is True because $A^-1= textadj( A)$ divided by $det(A)$ gives the same answer.
How can i provide a good justification for this?
linear-algebra matrices
edited Mar 14 at 15:45
gt6989b
35k22557
asked Mar 14 at 15:34
Sara RafiqSara Rafiq
245
$endgroup$
add a comment |
$begingroup$
The matrix $A=beginpmatrix -2 & 2 \ 1 & 3 endpmatrix$ is invertible with $A^-1=frac18 beginpmatrix-3 & 2\ 1 & 2 endpmatrix$.
(TRUE/FALSE)? In my opinion the answer is True because $A^-1= textadj( A)$ divided by $det(A)$ gives the same answer.
How can i provide a good justification for this?
linear-algebra matrices
edited Mar 14 at 15:45
gt6989b
35k22557
asked Mar 14 at 15:34
Sara RafiqSara Rafiq
245
$endgroup$
$begingroup$
Non-square matrices do not have an inverse, but in some cases may have a left inverse or right inverse
$endgroup$
– J. W. Tanner
Mar 14 at 15:37
1
$begingroup$
These are $2times2$ matrices, right? You can check by multiplying the two matrices.
$endgroup$
– kimchi lover
Mar 14 at 15:39
$begingroup$
@kimchilover Yes i would persume that
$endgroup$
– Sara Rafiq
Mar 14 at 15:44
add a comment |
$begingroup$
The matrix $A=beginpmatrix -2 & 2 \ 1 & 3 endpmatrix$ is invertible with $A^-1=frac18 beginpmatrix-3 & 2\ 1 & 2 endpmatrix$.
(TRUE/FALSE)? In my opinion the answer is True because $A^-1= textadj( A)$ divided by $det(A)$ gives the same answer.
How can i provide a good justification for this?
linear-algebra matrices
edited Mar 14 at 15:45
gt6989b
35k22557
asked Mar 14 at 15:34
Sara RafiqSara Rafiq
245
$endgroup$
The matrix $A=beginpmatrix -2 & 2 \ 1 & 3 endpmatrix$ is invertible with $A^-1=frac18 beginpmatrix-3 & 2\ 1 & 2 endpmatrix$.
(TRUE/FALSE)? In my opinion the answer is True because $A^-1= textadj( A)$ divided by $det(A)$ gives the same answer.
How can i provide a good justification for this?
linear-algebra matrices
linear-algebra matrices
edited Mar 14 at 15:45
gt6989b
35k22557
asked Mar 14 at 15:34
Sara RafiqSara Rafiq
245
edited Mar 14 at 15:45
gt6989b
35k22557
asked Mar 14 at 15:34
Sara RafiqSara Rafiq
245
edited Mar 14 at 15:45
gt6989b
35k22557
edited Mar 14 at 15:45
gt6989b
35k22557
edited Mar 14 at 15:45
gt6989b
35k22557
35k22557
asked Mar 14 at 15:34
Sara RafiqSara Rafiq
245
asked Mar 14 at 15:34
Sara RafiqSara Rafiq
245
asked Mar 14 at 15:34
Sara RafiqSara Rafiq
245
245
$begingroup$
Non-square matrices do not have an inverse, but in some cases may have a left inverse or right inverse
$endgroup$
– J. W. Tanner
Mar 14 at 15:37
1
$begingroup$
These are $2times2$ matrices, right? You can check by multiplying the two matrices.
$endgroup$
– kimchi lover
Mar 14 at 15:39
$begingroup$
@kimchilover Yes i would persume that
$endgroup$
– Sara Rafiq
Mar 14 at 15:44
add a comment |
$begingroup$
Non-square matrices do not have an inverse, but in some cases may have a left inverse or right inverse
$endgroup$
– J. W. Tanner
Mar 14 at 15:37
1
$begingroup$
These are $2times2$ matrices, right? You can check by multiplying the two matrices.
$endgroup$
– kimchi lover
Mar 14 at 15:39
$begingroup$
@kimchilover Yes i would persume that
$endgroup$
– Sara Rafiq
Mar 14 at 15:44
$begingroup$
Non-square matrices do not have an inverse, but in some cases may have a left inverse or right inverse
$endgroup$
– J. W. Tanner
Mar 14 at 15:37
$begingroup$
Non-square matrices do not have an inverse, but in some cases may have a left inverse or right inverse
$endgroup$
– J. W. Tanner
Mar 14 at 15:37
1
1
$begingroup$
These are $2times2$ matrices, right? You can check by multiplying the two matrices.
$endgroup$
– kimchi lover
Mar 14 at 15:39
$begingroup$
These are $2times2$ matrices, right? You can check by multiplying the two matrices.
$endgroup$
– kimchi lover
Mar 14 at 15:39
$begingroup$
@kimchilover Yes i would persume that
$endgroup$
– Sara Rafiq
Mar 14 at 15:44
$begingroup$
@kimchilover Yes i would persume that
$endgroup$
– Sara Rafiq
Mar 14 at 15:44
add a comment |
1 Answer
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$begingroup$
$$beginpmatrix-2&2\1&3endpmatrixbeginpmatrix-3&2\1&2endpmatrix=beginpmatrix8&0\0&8endpmatrix$$
answered Mar 14 at 15:39
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
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$begingroup$
$$beginpmatrix-2&2\1&3endpmatrixbeginpmatrix-3&2\1&2endpmatrix=beginpmatrix8&0\0&8endpmatrix$$
answered Mar 14 at 15:39
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
$begingroup$
$$beginpmatrix-2&2\1&3endpmatrixbeginpmatrix-3&2\1&2endpmatrix=beginpmatrix8&0\0&8endpmatrix$$
answered Mar 14 at 15:39
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
$begingroup$
$$beginpmatrix-2&2\1&3endpmatrixbeginpmatrix-3&2\1&2endpmatrix=beginpmatrix8&0\0&8endpmatrix$$
answered Mar 14 at 15:39
Yves DaoustYves Daoust
131k676229
$endgroup$
$$beginpmatrix-2&2\1&3endpmatrixbeginpmatrix-3&2\1&2endpmatrix=beginpmatrix8&0\0&8endpmatrix$$
answered Mar 14 at 15:39
Yves DaoustYves Daoust
131k676229
answered Mar 14 at 15:39
Yves DaoustYves Daoust
131k676229
answered Mar 14 at 15:39
Yves DaoustYves Daoust
131k676229
answered Mar 14 at 15:39
Yves DaoustYves Daoust
131k676229
131k676229
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$begingroup$
Non-square matrices do not have an inverse, but in some cases may have a left inverse or right inverse
$endgroup$
– J. W. Tanner
Mar 14 at 15:37
1
$begingroup$
These are $2times2$ matrices, right? You can check by multiplying the two matrices.
$endgroup$
– kimchi lover
Mar 14 at 15:39
$begingroup$
@kimchilover Yes i would persume that
$endgroup$
– Sara Rafiq
Mar 14 at 15:44