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Determine whether each of the following relations are reflexive, symmetric and transitive: Relation $R$ in the set $A$ of all human beings in a town at a particular time given by $R=\{(x,y):\; \text{x is the wife of y}\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Determine whether Relation $R$ is reflexive, symmetric and transitive: Relation $R$ in the set $A$ of all human beings in a town at a particular time given by $ R=\{(x,y):\; x$ is exactly $7\;cm$ taller than $y\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Determine whether Relation $R$ is reflexive, symmetric and transitive: Relation $R$ in the set $A$ of all human beings in a town at a particular time given by $R=\{(x,y):x\; \text{and y live in the same locality}\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Determine whether each of the following relations are reflexive, symmetric and transitive: Relation $R$ in the set $A$ of all human beings in a town at a particular time given by $\; R=\{(x,y):x $ and $y$ work at the same place $\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Determine whether Relation $R$ is reflexive, symmetric and transitive: Relation $R$ in the set $Z$ of all integers defined as $R=\{(x,y):x-y \;\; \text {is an integer}\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Determine whether Relation $R$ is reflexive, symmetric and transitive: Relation $R$ in the set $A = \{1,2,3,4,5,6\}$ defined as $R=\{(x,y):y \;\; \text {is divisible by } x\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Relation $R$ in a set $N$ of natural numbers defined as $R=\{(x,y):y=x+5$ and $x<4\}$. Which of the following is true about $R$?

asked Mar 7, 2013 by balaji.thirumalai

1 answer

Given Relation $R$ in the set $A=\{1,2,3,...,13,14\}$ defined as $R=\{(x,y):3x-y=0\}$. Which of the following is true?

asked Mar 7, 2013 by balaji.thirumalai

1 answer

Give an example of a relation which is (i) Symmetric but neither reflexive nor transitive.

asked Mar 7, 2013 by balaji.thirumalai

1 answer

If $\begin{bmatrix}xy & 4\\z+6 & x+y\end{bmatrix}=\begin{bmatrix}8 & w \\ 0 & 6\end{bmatrix}$ then find the value of x,y,z and w

asked Mar 7, 2013 by sreemathi.v

1 answer

Find inverse,by elementary row operations(if possible),of the following matrices$(ii)\quad\begin{bmatrix}1 &- 3\\-2 & 6\end{bmatrix}$

asked Mar 7, 2013 by sreemathi.v

1 answer

Find $ gof$ and $fog$, if $ f(x) = |\;x\;|$ , and $ g(x) = |\;5x-2\;| $

asked Mar 7, 2013 by meena.p

1 answer

Write Minors and Cofactors of the elements of following determinants: $ (ii) \quad \begin{vmatrix} 1&0&4 \\ 3&5&-1 \\ 0&1&2 \end{vmatrix} $

asked Mar 6, 2013 by sreemathi.v

1 answer

Write Minors and Cofactors of the elements of following determinants: $ \quad \begin{vmatrix} a&c \\ b&d \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

By using the properties of determinants show that $ (ii) \quad \begin{vmatrix} 1&1&1 \\ a&b&c \\ a^3&b^3&c^3 \end{vmatrix} = (a-b)(b-c)(c-a)(a+b+c) $

asked Mar 6, 2013 by sreemathi.v

1 answer

Find the values of $x$, if $ \text{: } \begin{vmatrix} 2&3 \\ 4&5 \end{vmatrix} = \begin{vmatrix} x&3 \\ 2x&5 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

Evaluate the determinants: $ \begin{vmatrix} 2&-1&2 \\ 0&2&-1 \\3&-5&0 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

Evaluate the determinants: $ \begin{vmatrix} 0&1&2 \\ -1&0&3 \\-2&3&0 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

Evaluate the determinants: $ \begin{vmatrix} 3&-4&5 \\ 1&1&-2 \\2&3&1 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

$ \text{Evaluate the determinants: } \text{(ii): } \begin{vmatrix} x^2-x+1&x-1\\x+1&x+1 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1 & 2\\4 & 1\\5 & 0\end{bmatrix},B=\begin{bmatrix}1 & 2\\6 & 4\\7 & 3\end{bmatrix},then\;verify\;that:(ii)\quad(A-B)'=A'-B'$.

asked Mar 6, 2013 by sreemathi.v

1 answer

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

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

Check the injectivity and surjectivity of the following functions: $f : Z\to Z$ given by $f(x)\; = x^3$

asked Mar 5, 2013 by meena.p

1 answer

Check the injectivity and surjectivity of the following functions: \(f : Z\to Z \;given\; by\; f(x)\; = x^2 \)

asked Mar 5, 2013 by meena.p

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

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

$(ii) If A = \begin{bmatrix} sin\alpha & cos\alpha \\ -cos\alpha & sin\alpha \end{bmatrix}$ 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

Each of the following defines a relation on $ N : (ii)\quad x+y=10,x,y\quad N$

asked Mar 4, 2013 by meena.p

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

Give an example of a map$(ii)\quad which\;is\;not\;one-one\;but\; not\; onto$

asked Mar 4, 2013 by meena.p

1 answer

Are the following set of ordered pairs function? If so,examine whether the mapping is injective or subjective $\;\{(a,b)\;:\;a\;$ is a person,$b\;$ is an ancestor of $a\}$

asked Mar 1, 2013 by meena.p

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: a) Rs. 1800.

asked Mar 1, 2013 by balaji.thirumalai

1 answer

Let A = $\begin{bmatrix} 1 & -2 & 1\\ -2 & 3 & 1\\ 1 & 1 & 5 \end{bmatrix}$. Verify that \[\] $(ii)\big(A^{-1}\big)^{-1}$

asked Mar 1, 2013 by sreemathi.v

1 answer

Show that: $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} $

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Show that: $(i) \qquad \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix}$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Find $X$ and $Y$ if: $(i) \quad X + Y = \begin{bmatrix} 7 & 0 \\ 2 & 5 \end{bmatrix} \text{ and } X - Y = \begin{bmatrix} 3 & 0 \\ 0 & 3 \end{bmatrix}$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Compute the indicated products: $(vi)\;\begin{bmatrix}3 & -1 &3\\-1 & 0 &2\end{bmatrix}\begin{bmatrix}2 & -3\\1 & 0\\3 & 1\end{bmatrix}$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Compute the indicated products: $(v)\;\begin{bmatrix}2 & 1\\3 & 2\\-1 & 1\end{bmatrix}\begin{bmatrix}1 & 0 &1\\-1 & 2 & 1\end{bmatrix}$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Compute the indicated products:$ (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} $

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Compute the indicated products: $(iii)\;\begin{bmatrix}1 & -2\\2 & 3\end{bmatrix}\begin{bmatrix}1 & 2 & 3\\2 & 3 & 1\end{bmatrix}$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Compute the indicated products: $(ii)\;\begin{bmatrix}1\\2\\3\end{bmatrix}\begin{bmatrix}2 & 3 & 4\end{bmatrix} $

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Compute the indicated products: $(i)\;\begin{bmatrix}a & b\\-b & a\end{bmatrix}\begin{bmatrix}a &-b\\b & a\end{bmatrix}$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Compute the following $ (iv)\;\begin{bmatrix}\cos^2x & \sin^2x\\ \sin^2x & \cos^2x\end{bmatrix}+\begin{bmatrix}\sin^2x & \cos^2x\\ \cos^2x & \sin^2x\end{bmatrix}$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

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