Recent questions tagged ch3

For the matrix $ A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix} $ , verify that $ (i) (A+A') $ is a symmetric matrix.

asked Nov 25, 2012 by pady_1

1 answer

Find $ \frac{1}{2}(A + A')$ and $\frac{1}{2}(A - A')$ , when $ A = \begin{bmatrix} 0 & a & b \\ -a & 0 & c \\ -b & -c & 0 \end{bmatrix} $

asked Nov 25, 2012 by pady_1

1 answer

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $ \quad \begin{bmatrix} 3 & 5 \\ 1 & -1 \end{bmatrix}$

asked Nov 25, 2012 by pady_1

1 answer

If $A, B$ are symmetric matrices of the same order, then $AB - BA$ is

asked Nov 23, 2012 by pady_1

1 answer

if $A = \begin{bmatrix} cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha \end{bmatrix} $ then $ A + A' = I, $ if the value of $\alpha$ is

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 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} 1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0 \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 & 3 \\ 2 & 2 & 3 \\ 3 & -2 & 2 \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 \\ 4 & 2 \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 \\ -1 & 2 \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} 6 & -3 \\ -2 & 1 \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 & -6 \\ 1 & -2 \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} 3 & -1 \\ -4 & 2 \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} 3 & 10 \\ 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} 4 & 5 \\ 3 & 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} 3 & 1 \\ 5 & 2 \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 & 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

1 answer

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

Matrices $A$ and $B$ will be inverse of each other only if

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 $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}$ prove that $A^n = \begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix} , n \in N$.

asked Nov 23, 2012 by pady_1

1 answer

If $ A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$ then prove that $ A^n = \begin{bmatrix} 1+2n & -4n \\ n & 1 - 2n \end{bmatrix} $ , where $n$ is any positive integer.

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

Find the values of $x, y, z $ if the matrix $ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} $ satisfy the equation $A'A = I $

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

A manufacturer produces three products $ x, y, z $ which he sells in two markets. Annual sales are indicated below: \[ \begin{array} { c c } \textbf{Market} & \textbf{Products} \\ I & 10,000 \quad 2,000 \quad 18,000 \\ II & 6,000 \quad 20,000 \quad 8,000 \end{array} \]
If unit sale prices of x, y and z are Rs 2.50, Rs 1.50 and Rs 1.00, respectively, find the total revenue in each market

asked Nov 22, 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 $A$ and $B$ are square matrices of the same order such that $AB = BA $, then prove by induction that $AB^n = B^nA $. Further, prove that $ (AB)^n = A^nB^n \: $ for all $ n ∈ N. $

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

For the matrix $ A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix} $ , verify that $ (i) (A+A') $ is a symmetric matrix.

Find $ \frac{1}{2}(A + A')$ and $\frac{1}{2}(A - A')$ , when $ A = \begin{bmatrix} 0 & a & b \\ -a & 0 & c \\ -b & -c & 0 \end{bmatrix} $

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $ \quad \begin{bmatrix} 3 & 5 \\ 1 & -1 \end{bmatrix}$

If $A, B$ are symmetric matrices of the same order, then $AB - BA$ is

if $A = \begin{bmatrix} cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha \end{bmatrix} $ then $ A + A' = I, $ if the value of $\alpha$ is

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3 \end{bmatrix} $

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0 \end{bmatrix} $

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

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

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

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 6 & -3 \\ -2 & 1 \end{bmatrix} $

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & -6 \\ 1 & -2 \end{bmatrix} $

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 3 & -1 \\ -4 & 2 \end{bmatrix} $

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 3 & 10 \\ 2 & 7 \end{bmatrix} $

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} $

Matrices $A$ and $B$ will be inverse of each other only if

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 $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}$ prove that $A^n = \begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix} , n \in N$.

If $ A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$ then prove that $ A^n = \begin{bmatrix} 1+2n & -4n \\ n & 1 - 2n \end{bmatrix} $ , where $n$ is any positive integer.

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.

Find the values of $x, y, z $ if the matrix $ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} $ satisfy the equation $A'A = I $

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 \(A\) and \(B\) are square matrices of the same order such that \(AB = BA \), then prove by induction that \(AB^n = B^nA \). Further, prove that \( (AB)^n = A^nB^n \: \) for all \( n ∈ N. \)

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: