Answers posted by sreemathi.v

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

answered Feb 15, 2013

Toolbox:There are six operations (transformations) on a matrix,three of which are due to rows and th...

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

answered Feb 15, 2013

Toolbox:There are six operations (transformations) on a matrix,three of which are due to rows and th...

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

answered Feb 15, 2013

Toolbox: There are six operations (transformations) on a matrix,three of which are due to rows an...

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

answered Feb 14, 2013

Toolbox: If A =$[a_{ij}]$ be an matrix,then the matrix obtained by interchanging the rows ...

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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:

answered Feb 14, 2013

Toolbox:Multiplication of two matrices is defined only if the number of columns of the left matrix i...

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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:

answered Feb 14, 2013

Toolbox:Multiplication of two matrices is defined only if the number of columns of the left matrix i...

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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.

answered Feb 14, 2013

Toolbox:With these type of word problems, we need to set up the correct matrix multiplication and so...

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

answered Feb 13, 2013

Toolbox:Multiplication of two matrices is defined only if the number of columns of the left matrix i...

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

answered Feb 13, 2013

Toolbox: Multiplication of two matrices is defined only if the number of columns of the le...

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

answered Feb 13, 2013

(i)Consider LHS $\begin{bmatrix}5 &-1\\6 & 7\end{bmatrix}\begin{bmatrix}...

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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 ). $

answered Feb 13, 2013

Toolbox:Given $ F( x ) = \begin{bmatrix} cos\;x & -sin\;x & 0 \\ sin\;x & cos\;x & 0...

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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 $w$.

answered Feb 13, 2013

Toolbox:The scalar multiplication $cA$ of a matrix $A$ and a number $c$ (also called a scalar in the...

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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} $

answered Feb 13, 2013

Toolbox:The sum / difference $A(+/-)B$ of two $m$-by-$n$ matrices $A$ and $B$ is calculated entrywis...

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

answered Feb 13, 2013

On addition:(i)$(x+y)+(x-y)=\begin{bmatrix} 7 & 0 \\ 2 & 5 \end{bmatrix}+\begin{bmatrix} 3 &...

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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}$\[Find\;each\;of\;the\;following:\]\[(i)\;A+B\qquad(ii)\;(A-B)\qquad(iii)\;3A-C\]\[(iv)\;AB\qquad(v)BA\]

answered Feb 12, 2013

(i)Since A & B are of the same order $2\times 2.$Hence addition of A&B is defined and g...

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

answered Feb 12, 2013

Toolbox: There are 9 elements in $3\times 3$ matrix and one element can be filled in two w...

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

answered Feb 12, 2013

Toolbox:A square matrix has equal number of rows and columns.In a square matrix, the number of rows ...

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

answered Feb 12, 2013

Toolbox: In general given a matrix $A_{3\times 4}$ its elements are given by $A=\begin{bma...

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

answered Feb 11, 2013

Toolbox:In general $a_{2\times 2}$ matrix is given by $\begin{bmatrix}a_{11} & a_{12}\\a_{21} &a...

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

answered Feb 11, 2013

Toolbox: $\Rightarrow $ If it has 18 elements. If a matrix is of order $m\times n$. ...

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

answered Feb 11, 2013

Toolbox: If a matrix is of order $m\times n.$ So the element of the matrix is $m\tim...

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

answered Feb 11, 2013

Toolbox: Order of matrix=A matrix having m rows and n column is called matrix of order $m\...

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Integrate the function $e^x\bigg(\frac{1+\sin x}{1+\cos x}\bigg)$

answered Feb 11, 2013

Toolbox: (i)$\int e^x\{f(x)+f'(x)\}dx=e^x(f(x))+c.$ (ii)$1+\sin x=\sin^2\frac{x}{2}+...

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Integrate the function $\;\int\;\frac{xe^x}{(1+x)^2}$

answered Feb 11, 2013

Toolbox: $\int e^x\{f(x)+f'(x)\}dx=e^xf(x)+c.$ Given $I=\int\frac {xe^x}{(1+x)^2}d...

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Integrate the function\[e^x(\sin x+\cos x)\]

answered Feb 11, 2013

Toolbox: $\int e^x\{f(x)+f'(x)\}dx=e^xf(x)+c.$ Given $I=\int e^x(\sin x+\cos x).$ ...

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Integrate the function $\;\int\;(x^2+1)\;log\;x$

answered Feb 11, 2013