Recent questions in Matrices

$A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}\;and\;B=\begin{bmatrix}4 & 0\\1 & 3\\2 & 6\end{bmatrix},then\;verify \;that:(iii)\quad(KA)'=(KA')$

asked Mar 6, 2013 by sreemathi.v

1 answer

$A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}\;and\;B=\begin{bmatrix}4 & 0\\1 & 3\\2 & 6\end{bmatrix},then\;verify \;that:(ii)\quad(AB)'=B'A'$

asked Mar 6, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1 & 2\\-2 & 1\end{bmatrix},B=\begin{bmatrix}2 & 3\\3 & -4\end{bmatrix}\;and\;C=\begin{bmatrix}1 & 0\\-1 & 0\end{bmatrix},verify:(ii)\;A(B+C)=AB+AC$

asked Mar 5, 2013 by sreemathi.v

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 the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50 paise respectively. Find the gross profit.

asked Mar 5, 2013 by balaji.thirumalai

1 answer

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $(iv) \begin{bmatrix} 1 & 5 \\ -1 & 2 \end{bmatrix}$

asked Mar 5, 2013 by balaji.thirumalai

1 answer

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $(iii) \begin{bmatrix} 3 & 3 & -1 \\ -2 & -2 & 1 \\ -4 & -5 & 2 \end{bmatrix}$

asked Mar 5, 2013 by balaji.thirumalai

1 answer

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $(ii) \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix}$

asked Mar 5, 2013 by balaji.thirumalai

1 answer

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

asked Mar 5, 2013 by balaji.thirumalai

1 answer

$(ii)$ Show that the matrix $A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix}$ is a skew symmetric matrix. $

asked Mar 5, 2013 by balaji.thirumalai

1 answer

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

asked Mar 5, 2013 by balaji.thirumalai

1 answer

For the matrices $A$ and $B$ , verify that $(AB)' = B'A'$ , where $\text{ (ii) } A = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix} \text{ , } B = \begin{bmatrix} 1 & 5 & 7 \end{bmatrix}$

asked Mar 5, 2013 by balaji.thirumalai

1 answer

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

asked Mar 5, 2013 by balaji.thirumalai

1 answer

If $A = \begin{bmatrix} -1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} -4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1 \end{bmatrix}$ then verify that $(ii) (A-B)' = A' - B'$

asked Mar 5, 2013 by balaji.thirumalai

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 a matrix $Z$ such that $X+Y+Z$ is a zero matrix.

asked Mar 4, 2013 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 $2X-3Y$

asked Mar 4, 2013 by sreemathi.v

1 answer

Construct $a_{2\times 2}$ matrix where $a_{ij} =|2i+3j|$

asked Mar 4, 2013 by sreemathi.v

1 answer

In the matrix $A=\begin{bmatrix} a & 1 & x \\ 2 & \sqrt 3 & x^2 y \\ 0 & 5 & \frac{2}{5} \end{bmatrix}$ , write the elements $a_{23}$ , $a_{31}$ , $a_{12}$

asked Mar 4, 2013 by sreemathi.v

1 answer

In the matrix $A=\begin{bmatrix} a & 1 & x \\ 2 & \sqrt 3 & x^2 y \\ 0 & 5 & \frac{2}{5} \end{bmatrix} write:(ii) Element\; of \;the\; matrices.$

asked Mar 4, 2013 by sreemathi.v

1 answer

(iii) Find the transpose of the matrix $\begin{bmatrix} -1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1 \end{bmatrix}$

asked Mar 1, 2013 by sharmaaparna1

1 answer

Find the transpose of the following matrices: $\begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix}$

asked Mar 1, 2013 by balaji.thirumalai

1 answer

Find the transpose of each of the following matrices : $(i) \begin{bmatrix} 5 \\ \tfrac{1}{2} \\ -1 \end{bmatrix}$

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: b) Rs. 2000

asked Mar 1, 2013 by balaji.thirumalai

1 answer