Recent questions tagged bookproblem

Find the approximate value of $f (5.001)$, where $f (x) = x^3 – 7x^2 + 15.$

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Find the approximate value of $ f (2.01)$, where $f (x) = 4x^2 + 5x + 2$.

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(i)\;\sqrt{25.3}$

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the line $y = x + 1$ is a tangent to the curve $y^2 = 4x$ at the point

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the slope of the normal to the curve $ y = 2x^2 + 3 \sin\: x$ at $x = 0$ is

asked Nov 26, 2012 by thanvigandhi_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

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