Recent questions tagged shortanswer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 4 & 5 \\ 3 & 4 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

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Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 3 & 1 \\ 5 & 2 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

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Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 3 \\ 5 & 7 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 1 & 3 \\ 2 & 7 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 1 \\ 1 & 1 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

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Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Let $A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} $, show that $ (aI + bA)^n = a^nI + na^{n-1}bA $, where $\;I\;$ is the identity matrix of order 2 and $n \in N$.

asked Nov 23, 2012 by pady_1

1 answer

If $A$ and $B$ are symmetric matrices, prove that $AB - BA$ is a skew symmetric matrix.

asked Nov 23, 2012 by pady_1

1 answer

Show that the matrix $B'AB$ is symmetric or skew symmetric according as A is symmetric or skew symmetric.

asked Nov 23, 2012 by pady_1

1 answer

For what values of $x$,
$\begin{bmatrix} 1 & 2 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2 \end{bmatrix} \begin{bmatrix} 0 \\ 2 \\ x \end{bmatrix}$ = 0 ?

asked Nov 23, 2012 by pady_1

1 answer

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix} $ show that $A^2 - 5A + 7I = 0$

asked Nov 23, 2012 by pady_1

1 answer

Find $x$, if $ \begin{bmatrix} x & -5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} = 0 $

asked Nov 23, 2012 by pady_1

1 answer

Find the matrix $ X $ so that $ X \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \: = \: \begin{bmatrix} -7 & -8 & -9 \\ 2 & 4 & 6 \end{bmatrix} $

asked Nov 22, 2012 by pady_1

1 answer

If the matrix A is both symmetric and skew symmetric, then

asked Nov 22, 2012 by pady_1

1 answer

If $A $ is a square matrix, such that $ A^2 = A $ , then $ (1 + A )^3 - 7A $ is equal to:

asked Nov 22, 2012 by pady_1

1 answer

Ask Questions, Get Answers

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 4 & 5 \\ 3 & 4 \end{bmatrix} $

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 3 & 1 \\ 5 & 2 \end{bmatrix} $

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} $

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix} $

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 3 \\ 5 & 7 \end{bmatrix} $

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 1 & 3 \\ 2 & 7 \end{bmatrix} $

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 1 \\ 1 & 1 \end{bmatrix} $

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix} $

Let $A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} $, show that $ (aI + bA)^n = a^nI + na^{n-1}bA $, where $\;I\;$ is the identity matrix of order 2 and $n \in N$.

If $A$ and $B$ are symmetric matrices, prove that $AB - BA$ is a skew symmetric matrix.

Show that the matrix $B'AB$ is symmetric or skew symmetric according as A is symmetric or skew symmetric.

For what values of $x$,
$\begin{bmatrix} 1 & 2 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2 \end{bmatrix} \begin{bmatrix} 0 \\ 2 \\ x \end{bmatrix}$ = 0 ?

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix} $ show that $A^2 - 5A + 7I = 0$

Find $x$, if $ \begin{bmatrix} x & -5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} = 0 $

Find the matrix \( X \) so that \( X \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \: = \: \begin{bmatrix} -7 & -8 & -9 \\ 2 & 4 & 6 \end{bmatrix} \)

If the matrix A is both symmetric and skew symmetric, then

If $A $ is a square matrix, such that $ A^2 = A $ , then $ (1 + A )^3 - 7A $ is equal to: