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Recent questions tagged p82

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: b) Rs. 2000

asked Mar 1, 2013 by balaji.thirumalai

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: a) Rs. 1800.

asked Mar 1, 2013 by balaji.thirumalai

1 answer

The value of the determinant $\begin{vmatrix}x & x+y & x+2y\\x+2y & x & x+y\\x+y & x+2y & x\end{vmatrix}$ is

asked Dec 27, 2012 by sreemathi.v

1 answer

If $x,y,z$ are all different from zero and $\begin{vmatrix}1+x & 1 & 1\\1 & 1+y & 1\\1 & 1 & 1+z\end{vmatrix}$ = 0, then value of $x^{-1}+y^{-1}+z^{-1}$ is

asked Dec 27, 2012 by sreemathi.v

1 answer

If A and B are invertible matrices,then which of the following is not correct?\[\begin{array}{1 1}(A)\quad adjA=|A|.A^{-1} & (B)\quad det(A)^{-1}=[det(A)]^{-1}\\(C)\quad (AB)^{-1}=B^{-1}A^{-1} & (D)\quad (A+B)^{-1}=B^{-1}+A^{-1}\end{array}\]

asked Dec 27, 2012 by sreemathi.v

1 answer

If $A=\begin{vmatrix}2 & \lambda & 3\\0 & 2 & 5\\1 & 1 & 3\end{vmatrix},$ then$\;A^{-1}\;$exists if $\lambda = ?$

asked Dec 27, 2012 by sreemathi.v

1 answer

If $f(x)=\begin{vmatrix}0 & x-a & x-b\\x-a & 0 & x-c\\x-b & x-c & 0\end{vmatrix},then$\[\begin{array}{1 1}(A)\quad f(a)=0 & (B)\quad f(b)=0\\(C)\quad f(0)=0 & (D)\quad f(1)=0\end{array}\]

asked Dec 27, 2012 by sreemathi.v

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

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