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Recent questions tagged ch3

Find non-zero values of $x$ satisfying the matrix equation $x\begin{bmatrix}2x & 2\\3 & x\end{bmatrix}+2\begin{bmatrix}8 & 5x\\4 & 4x\end{bmatrix}=2\begin{bmatrix}(x^2+8) & 24\\(10) & 6x\end{bmatrix}$

asked Dec 22, 2012 by sreemathi.v

1 answer

If $X=\begin{bmatrix}3 & 1 & 1\\5 & 2 & 3\end{bmatrix}$ and $Y=\begin{bmatrix}2 & 1 & 1\\7 & 2 & 4\end{bmatrix}$, find $X + Y$

asked Dec 22, 2012 by sreemathi.v

1 answer

If possible,find the sum of the matrices A and B,where $A=\begin{bmatrix}\sqrt 3 & 1\\2 & 3\end{bmatrix},and\; B=\begin{bmatrix}x & y & z\\a & b &6\end{bmatrix}$

asked Dec 22, 2012 by sreemathi.v

1 answer

Find values of a and b if A=B,where A=$\begin{bmatrix}a + 4 & 3b\\8 & - 6\end{bmatrix},B=\begin{bmatrix}2a + 2 & b^2 + 2\\8 & b^2 - 5b\end{bmatrix}$

asked Dec 22, 2012 by sreemathi.v

1 answer

Construct a $3\times 2$ matrix whose elements are given by $a_{ij}=e^{i.x}\sin jx$

asked Dec 22, 2012 by sreemathi.v

1 answer

Construct $a_{2\times 2}$ matrix where $a_{ij} =\frac{(i + 2j)^2}{2}$

asked Dec 22, 2012 by sreemathi.v

1 answer

What is the order of the matrix $A=\begin{bmatrix} a & 1 & x \\ 2 & \sqrt 3 & x^2 y \\ 0 & 5 & \frac{2}{5} \end{bmatrix}$

asked Dec 21, 2012 by sreemathi.v

1 answer

If a matrix has 28 elements, what are the possible orders it can have?

asked Dec 21, 2012 by sreemathi.v

1 answer

Find the value of x, if $\begin {bmatrix} 3x+y & -y \\ 2y-x & 3 \end{bmatrix} = \begin {bmatrix} 1 & 2 \\ -5 & 3 \end{bmatrix} $

asked Dec 20, 2012 by thanvigandhi_1

1 answer

Find the value of $x$ and $y$ if : $ 2\begin{bmatrix} 1 & 3 \\[0.3em] 0 & x \\[0.3em] \end{bmatrix} + \begin{bmatrix} y & 0 \\[0.3em] 1 & 2 \\[0.3em] \end{bmatrix} = \begin{bmatrix} 5 & 6 \\[0.3em] 1 & 8 \\[0.3em] \end{bmatrix}$

asked Dec 20, 2012 by thanvigandhi_1

1 answer

Let $ A = \begin{bmatrix} 3 & 2 & 5 \\[0.3em] 4 & 1 & 3 \\[0.3em] 0 & 6 & 7 \end{bmatrix}$ Express $A$ as sum of two matrices such that one is symmetric and the other is skew symmetric.

asked Dec 20, 2012 by thanvigandhi_1

1 answer

Compute the indicated products\begin{array}{1 1 1}(i)\;\begin{bmatrix}a & b\\-b & a\end{bmatrix}\begin{bmatrix}a &-b\\b & a\end{bmatrix}\;(ii)\;\begin{bmatrix}1\\2\\3\end{bmatrix}\begin{bmatrix}2 & 3 & 4\end{bmatrix} & (iii)\;\begin{bmatrix}1 & -2\\2 & 3\end{bmatrix}\begin{bmatrix}1 & 2 & 3\\2 & 3 & 1\end{bmatrix}\\(iv)\;\begin{bmatrix}2 & 3 &4\\3 & 4 &4\\4 & 5 & 6\end{bmatrix}\begin{bmatrix}1 & -3 & 5\\0 & 2 &4\\3 & 0 & 5\end{bmatrix} & (v)\;\begin{bmatrix}2 & 1\\3 & 2\\-1 & 1\end{bmatrix}\begin{bmatrix}1 & 0 &1\\-1 & 2 & 1\end{bmatrix}\\(vi)\;\begin{bmatrix}3 & -1 &3\\-1 & 0 &2\end{bmatrix}\begin{bmatrix}2 & -3\\1 & 0\\3 & 1\end{bmatrix}\end{array}

asked Dec 7, 2012 by sreemathi.v

1 answer

In the matrix $A=\begin{bmatrix}2 & 5 & 19 & -7\\35 & -2 & \frac{5}{2} & 12\\\sqrt 3 & 1 & -5& 17\end{bmatrix},$write:\[(i)\;The\;order\;of\;the\;matrix,\qquad(ii)\;The\;number\;of\;the\;elements,\]\[(iii)\;Write\;the\;elements\;a_{13},a_{21},a_{33},a_{24},a_{23}\]

asked Dec 7, 2012 by sreemathi.v

1 answer

If a matrix has 24 elements,what are the possible orders it can have? What, if it has 13 elements?

asked Dec 7, 2012 by sreemathi.v

1 answer

If a matrix has 18 elements,what are the possible orders it can have?What, if it has 5 elements?

asked Dec 7, 2012 by sreemathi.v

1 answer

Construct a 2 x 2 matrix, $A=[a_{ij}],$whose elements are given by: $\;a_{ij}=\frac{(i+2j)^2}{2}$

asked Dec 7, 2012 by sreemathi.v

1 answer

Construct a 3 x 4 matrix,whose elements are given by: $\;a_{ij}=2i-j$

asked Dec 7, 2012 by sreemathi.v

1 answer

Find the values of x,y and z from the following equations:\[(i)\begin{bmatrix}4 & 3\\x & 5\end{bmatrix}=\begin{bmatrix}y & z\\1 & 5\end{bmatrix}\qquad(ii)\;\begin{bmatrix}x+y & z\\5+z & xy\end{bmatrix}=\begin{bmatrix}6 & 2\\5 & 8\end{bmatrix}\qquad(iii)\;\begin{bmatrix}x+y+z\\x+z\\y+z\end{bmatrix}=\begin{bmatrix}9\\5\\7\end{bmatrix}\]

asked Dec 7, 2012 by sreemathi.v

1 answer

Find the values of a,b,c and d from the question:
$\begin{bmatrix}a-b & 2a+c\\2a-b & 3c+d\end{bmatrix}$ = $\begin{bmatrix}-1 & 5\\0 & 13\end{bmatrix}$

asked Dec 7, 2012 by sreemathi.v

1 answer

$A=[a_{ij}]_{m \times n}$ is a square matrix if

asked Dec 7, 2012 by sreemathi.v

1 answer

Which of the given values of x and y make the following pair of matrices equal:$\begin{bmatrix}3x+7 & 5\\y+1 & 2-3x\end{bmatrix},\begin{bmatrix}0 & y-2\\8 & 4\end{bmatrix} $

asked Dec 7, 2012 by sreemathi.v

1 answer

The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is:

asked Dec 7, 2012 by sreemathi.v

2 answers

Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$\[Find\;each\;of\;the\;following:\]\[(i)\;A+B\qquad(ii)\;(A-B)\qquad(iii)\;3A-C\]\[(iv)\;AB\qquad(v)BA\]

asked Dec 7, 2012 by sreemathi.v

1 answer

Compute the following $\;\begin{bmatrix}a^2+b^2 & b^2+c^2\\a^2+c^2 & a^2+b^2\end{bmatrix}+\begin{bmatrix}2ab & 2bc\\-2ac & 2ab\end{bmatrix}$

asked Dec 6, 2012 by sreemathi.v

1 answer

If $ A = \begin{bmatrix} 1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1 \end{bmatrix} , B = \begin{bmatrix} 3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3 \end{bmatrix} \text{ and } C = \begin{bmatrix} 4 & 1 & 2 \\ 0 & 3 & 2 \\ 1 & -3 & 2 \end{bmatrix} $, then compute $( A + B )$ and $( B - C )$. Also verify that $A + ( B - C ) = ( A + B ) - C. $

asked Nov 26, 2012 by pady_1

1 answer

If $ A = \begin{bmatrix} \frac{2}{3} & 1 & \frac{5}{3} \\ \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \\ \frac{7}{3} & 2 & \frac{2}{3} \end{bmatrix} \text{ and } B = \begin{bmatrix} \frac{2}{5} & \frac{3}{5} & 1 \\ \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \\ \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{bmatrix} \text{ then compute } 3A - 5B $

asked Nov 26, 2012 by pady_1

1 answer

Simplify $\cos\theta\begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$ + $\sin\theta\begin{bmatrix} \sin\theta & -\cos\theta \\ \cos\theta & \sin\theta \end{bmatrix} $

asked Nov 26, 2012 by pady_1

1 answer

Find $X$ and $Y$ if $$ \begin{array}{l \qquad l} (i) \quad X + Y = \begin{bmatrix} 7 & 0 \\ 2 & 5 \end{bmatrix} \text{ and } X - Y = \begin{bmatrix} 3 & 0 \\ 0 & 3 \end{bmatrix} \\ (ii) \quad 2X + 3Y = \begin{bmatrix} 2 & 3 \\ 4 & 0 \end{bmatrix} \text{ and } 3X + 2Y = \begin{bmatrix} 2 & -2 \\ -1 & 5 \end{bmatrix} \end{array} $$

asked Nov 26, 2012 by pady_1

1 answer

Find $X$ , if $Y = \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix} $ and $ 2X + Y = \begin{bmatrix} 1 & 0 \\ -3 & 2 \end{bmatrix} $

asked Nov 26, 2012 by pady_1

1 answer

Find $x$ and $y$, if $ 2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} $

asked Nov 26, 2012 by pady_1

1 answer

Solve the equation for $x, y, z$ and $t$ if $ 2\begin{bmatrix}x & z \\ y & t \end{bmatrix} + 3\begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix} = 3\begin{bmatrix} 3 & 5 \\ 4 & 6 \end{bmatrix} $

asked Nov 26, 2012 by pady_1

1 answer

If $ x\begin{bmatrix} 2 \\ 3 \end{bmatrix} + y\begin{bmatrix} -1 \\ 1 \end{bmatrix} = \begin{bmatrix} 10 \\ 5 \end{bmatrix} $, find the values of $x$ and $y$.

asked Nov 25, 2012 by pady_1

1 answer

Given $3\begin{bmatrix} x & y \\ z & w \end{bmatrix}$ = $\begin{bmatrix} x & 6 \\ -1 & 2w \end{bmatrix}$ + $\begin{bmatrix} 4 & x + y \\ z + w & 3 \end{bmatrix}$, find the values of $x, y, z$ and $w$.

asked Nov 25, 2012 by pady_1

1 answer

if $ F( x ) = \begin{bmatrix} cos\;x & -sin\;x & 0 \\ sin\;x & cos\;x & 0 \\ 0 & 0 & 1 \end{bmatrix}, $ show that $ F( x )\; F( y ) = F( x + y ). $

asked Nov 25, 2012 by pady_1

1 answer

Show that $$ \begin{array}{l} (i) \qquad \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix} \\[0.5em] (ii) \qquad \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \end{array} $$

asked Nov 25, 2012 by pady_1

1 answer

Find $ A^2 -5A + 6I $ , if $ A = \begin{bmatrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{bmatrix} $

asked Nov 25, 2012 by pady_1

1 answer

if $ A = \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} ,$ prove that $ A^3 - 6A^2 + 7A + 2I = 0 $

asked Nov 25, 2012 by pady_1

1 answer

If $ A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix} $ and $ I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $ find $k$ so that $A^2 = kA - 2I$

asked Nov 25, 2012 by pady_1

1 answer

If $ A = \begin{bmatrix} 0 & -tan \frac{\alpha}{2} \\ tan\frac{\alpha}{2} & 0 \end{bmatrix} $ and $I$ is the identity matrix of order $2$, show that $ I + A = ( I - A ) \begin{bmatrix} cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha \end{bmatrix} $

asked Nov 25, 2012 by pady_1

1 answer

A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of: $$ \text{(a) Rs 1800} \qquad \qquad \text{(b) Rs 2000} $$

asked Nov 25, 2012 by pady_1

1 answer

The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

asked Nov 25, 2012 by pady_1

1 answer

Assume $X, Y, Z, W$ and $P$ are matrices of order $2\times n, 3\times k, 2\times p, n\times 3$ and $p\times k$, respectively. The restriction on $n, p, k$ so that $PY + WY$ will be defined are:

asked Nov 25, 2012 by pady_1

1 answer

Assume $X, Y, Z, W$ and $P$ are matrices of order $2\times n$, $3\times k$, $2\times p$, $n\times 3$ and $p\times k$, respectively. If $n = p$ then the order of the matrix $7X - 5Z$ is:

asked Nov 25, 2012 by pady_1

1 answer

Find the transpose of each of the following matrices : $$ \text{ (i) } \begin{bmatrix} 5 \\ \tfrac{1}{2} \\ -1 \end{bmatrix} \qquad \qquad (ii) \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix} \qquad \qquad (iii)\begin{bmatrix} -1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1 \end{bmatrix} $$

asked Nov 25, 2012 by pady_1

1 answer

if $ A = \begin{bmatrix} -1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1 \end{bmatrix} \text{, then verify that } $ $$ \text{ (i) } (A+B)' = A' + B' $$

asked Nov 25, 2012 by pady_1

1 answer

If $ A' = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -1 & 2 &1 \\ 1 & 2 & 3 \end{bmatrix} \text{ , then verify that } $$ \text{ (i) } (A + B )' = A' + B' \qquad \qquad $

asked Nov 25, 2012 by pady_1

1 answer

If $A' = \begin{bmatrix} -2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 0 \\ 1 & 2 \end{bmatrix}$, then find $(A + 2B)'$

asked Nov 25, 2012 by pady_1

1 answer

For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (i) } A = \begin{bmatrix} 1 \\ -4 \\ 3 \end{bmatrix} \text{ , } B = \begin{bmatrix} -1 & 2 & 1 \end{bmatrix} \qquad $$

asked Nov 25, 2012 by pady_1

1 answer

$ (i) A = \begin{bmatrix} cos\alpha & sin\alpha \\ -sin\alpha & cos\alpha \end{bmatrix}$ then verify that $A'A = I$

asked Nov 25, 2012 by pady_1

1 answer

$ (i)$ Show that the matrix $A = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix}$ is a symmetric matrix.

asked Nov 25, 2012 by pady_1

1 answer

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