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Recent questions tagged easy

Which of the following is an example of matrices A,B and C such that AB=AC,where A is non-zero matrix,but $B\neq C.$

asked Dec 22, 2012 by sreemathi.v

1 answer

If A=[3 , 5],B=[7, 3],then find a non-zero matrix C such that AC=BC.

asked Dec 22, 2012 by sreemathi.v

1 answer

If X and Y are $2\times 2$matrices,then solve the following matrix equation for X and Y\[2X+3Y=\begin{bmatrix}2 & 3\\4 & 0\end{bmatrix},3X+2Y=\begin{bmatrix}-2 & 2\\1 & -5\end{bmatrix}.\]

asked Dec 22, 2012 by sreemathi.v

1 answer

Solve for x and y:\[x\begin{bmatrix}2\\1\end{bmatrix}+y\begin{bmatrix}3\\5\end{bmatrix}+\begin{bmatrix}-8\\-11\end{bmatrix}=0\]

asked Dec 22, 2012 by sreemathi.v

1 answer

Given $A=\begin{bmatrix}2 & 4 & 0\\3 & 9 & 6\end{bmatrix}\;and\;B=\begin{bmatrix}1& 4\\2 & 8\\1 & 3\end{bmatrix}.\;Is \;(AB)'=B'A'?$

asked Dec 22, 2012 by sreemathi.v

1 answer

Show by an example that for $A\neq 0,B\neq 0,AB=0.$

asked Dec 22, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}3 & -4\\1 & 1\\2 & 0\end{bmatrix}\;and\;B=\begin{bmatrix}2 & 1 & 2\\1 & 2 & 4\end{bmatrix} \;$ then verify that $(BA)^2\neq B^2A^2$

asked Dec 22, 2012 by sreemathi.v

1 answer

Find A,if $\begin{bmatrix}4\\1\\3\end{bmatrix}A=\begin{bmatrix}4 & 8 & 4\\1 & 2 &1\\3 & 6 & 3\end{bmatrix}$

asked Dec 22, 2012 by sreemathi.v

1 answer

Find the matrix A satisfying the matrix equation $\begin{bmatrix}2 & 1\\3 & 2\end{bmatrix}A\begin{bmatrix}3 & 2\\5 & 3\end{bmatrix}=\begin{bmatrix}1 & 0\\0 & 12\end{bmatrix}$

asked Dec 22, 2012 by sreemathi.v

1 answer

Find the value of $x$ if $\begin{bmatrix}1 & x &1\end{bmatrix}\begin{bmatrix}1 & 3 & 2\\2 & 5 & 1\\15 & 3 & 2\end{bmatrix}\begin{bmatrix}1\\2\\x\end{bmatrix}=0$.

asked Dec 22, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}0 & 1\\1& 1\end{bmatrix}\;and\;B=\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix},\;show\;that\;(A+B)(A-B)\neq A^2-B^2$

asked Dec 22, 2012 by sreemathi.v

1 answer

Find non-zero values of $x$ satisfying the matrix equation $x\begin{bmatrix}2x & 2\\3 & x\end{bmatrix}+2\begin{bmatrix}8 & 5x\\4 & 4x\end{bmatrix}=2\begin{bmatrix}(x^2+8) & 24\\(10) & 6x\end{bmatrix}$

asked Dec 22, 2012 by sreemathi.v

1 answer

If possible,find the sum of the matrices A and B,where $A=\begin{bmatrix}\sqrt 3 & 1\\2 & 3\end{bmatrix},and\; B=\begin{bmatrix}x & y & z\\a & b &6\end{bmatrix}$

asked Dec 22, 2012 by sreemathi.v

1 answer

Find values of a and b if A=B,where A=$\begin{bmatrix}a + 4 & 3b\\8 & - 6\end{bmatrix},B=\begin{bmatrix}2a + 2 & b^2 + 2\\8 & b^2 - 5b\end{bmatrix}$

asked Dec 22, 2012 by sreemathi.v

1 answer

Construct a $3\times 2$ matrix whose elements are given by $a_{ij}=e^{i.x}\sin jx$

asked Dec 22, 2012 by sreemathi.v

1 answer

If a matrix has 28 elements, what are the possible orders it can have?

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: The value of the expression $(\cos^{-1}x)^2$ is equal to $\sec^2x.$

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: All trigonometric functions have inverse over their respective domains.

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\cot^{-1}(-x)$ for all $x\;\in\;R$ in terms of $\cot^{-1}x$ is ____________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The result $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\bigg(\Large {\frac{x-y}{1+xy}}\normalsize \bigg)$ is true when value of xy is _____________.

asked Dec 21, 2012 by sreemathi.v

1 answer

If $y=2\tan^{-1}x+\sin^{-1}\frac{2x}{1+x^2}$ for all x,then _< y < ___.

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of expression $\tan\bigg(\Large \frac{\sin^{-1}x+\cos^{-1}x}{2} \normalsize\bigg),when\;x=\frac{\sqrt 3}{2}$ is _______________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\cos(\sin^{-1}x+\cos^{-1}x),|x|\leq 1$ is _____________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\cos^{-1}\bigg(\cos\frac{14\pi}{3}\bigg)$ is _____________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The principal value of $ \tan^{-1}\sqrt 3 $ is _______________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The set of values of $\sec^{-1}\big(\frac{1}{2}\big)$ is ______________.

asked Dec 21, 2012 by sreemathi.v

1 answer

If $\cos(\tan^{-1}x+\cot^{-1}\sqrt 3)=0,$then the value of $x$ is _______________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\sin^{-1}\bigg(\sin\frac{3\pi}{5}\bigg)$ is ________________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The principal value of $\cos^{-1}\bigg(-\Large {\frac{1}{2}}\normalsize \bigg)$ is_____________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The number of real solutions of the equation$\sqrt{1+\cos2x}=\sqrt 2\cos^{-1}(\cos x)\;in\begin{bmatrix}\frac{\Large \pi}{2},\pi\end{bmatrix}$

asked Dec 21, 2012 by sreemathi.v

1 answer

If $|\;x\;|\leq 1,then\;2\tan^{-1}x+\sin^{-1}\frac{2x}{1+x^2}$ is equal to:

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\cot\bigg(\cos^{-1}\frac{7}{25}\bigg)$ is

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of the expression $2\sec^{-1}2+\sin^{-1}\frac{1}{2}$ is:

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\cos^{-1}\bigg(\cos\frac{3\pi}{2}\bigg)$ is equal to:

asked Dec 21, 2012 by sreemathi.v

1 answer

The domain of the function defined by $f(x)=\sin^{-1}\sqrt{x-1}$ is

asked Dec 20, 2012 by sreemathi.v

1 answer

The domain of the function $\cos^{-1}(2x-1)$ is

asked Dec 20, 2012 by sreemathi.v

1 answer

If $3\tan^{-1}x+\cot^{-1}x=\pi$ then $x$ equals

asked Dec 20, 2012 by sreemathi.v

1 answer

Which of the following is the principal value branch of $\text{cosec}^{-1}x$?

asked Dec 20, 2012 by sreemathi.v

1 answer

Which of the following is the principal value branch of $\cos^{-1}x$?

asked Dec 20, 2012 by sreemathi.v

1 answer

Find the value of x, if $\begin {bmatrix} 3x+y & -y \\ 2y-x & 3 \end{bmatrix} = \begin {bmatrix} 1 & 2 \\ -5 & 3 \end{bmatrix} $

asked Dec 20, 2012 by thanvigandhi_1

1 answer

Prove that $ \sin^{-1}{\frac{8}{17}}+\sin^{-1}{\frac{3}{5}}=\sin^{-1}{\frac{77}{85}}$

asked Dec 20, 2012 by sreemathi.v

1 answer

Find the value of $\tan^{-1}\bigg(\tan{\frac{2\pi}{3}}\bigg)$

asked Dec 20, 2012 by sreemathi.v

1 answer

Find the value of $x$ and $y$ if : $ 2\begin{bmatrix} 1 & 3 \\[0.3em] 0 & x \\[0.3em] \end{bmatrix} + \begin{bmatrix} y & 0 \\[0.3em] 1 & 2 \\[0.3em] \end{bmatrix} = \begin{bmatrix} 5 & 6 \\[0.3em] 1 & 8 \\[0.3em] \end{bmatrix}$

asked Dec 20, 2012 by thanvigandhi_1

1 answer

Let n be a fixed positive integer.Define a relation R in Z as follows: a,b E\inE Z, aRb if and only if a-b is divisible by n. Show that R is an equivalence relation.

asked Dec 20, 2012 by sreemathi.v

1 answer

Let $ A = \begin{bmatrix} 3 & 2 & 5 \\[0.3em] 4 & 1 & 3 \\[0.3em] 0 & 6 & 7 \end{bmatrix}$ Express $A$ as sum of two matrices such that one is symmetric and the other is skew symmetric.

asked Dec 20, 2012 by thanvigandhi_1

1 answer

Let $f\;:\;R\rightarrow R$ be the function defined by $f(x)=\frac{1}{2-\cos x}\forall x\;\in R.$Then,find the range of f.

asked Dec 18, 2012 by sreemathi.v

1 answer

If functions $f\;:\;A \rightarrow B\;and\;g\;:\;B \rightarrow A $ satisfy g o f =$I_A$ ,then is f one-one and g onto

asked Dec 18, 2012 by sreemathi.v

1 answer

Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$\quad f=\{(1,4),(1,5),(2,4),(3,5)\} $

asked Dec 18, 2012 by sreemathi.v

1 answer

Let the function $f\;:\;R \rightarrow R$ be defined by$ f(x)=\cos x,\forall \;x\;\in R$.Show that f is neither one-one nor onto

asked Dec 18, 2012 by sreemathi.v

1 answer

Let C be the set of complex numbers.Prove that the mapping $f\; :\;C \rightarrow R\;given\;by\;f(z)=|\;z\;|,\forall\; z \in C,$is neither one-one nor onto.

asked Dec 18, 2012 by sreemathi.v

1 answer

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