Recent questions tagged p10

Gravel is being dumped from a conveyor belt at a rate of $30\;ft^{3}/min$ and its coarsened such that it forms a pile in the shape of the cone whose base diameter and hight are always equal. How fast is the hight of the pile increasing when the pile is $10$ ft hight?

asked May 1, 2013 by poojasapani_1

1 answer

For $A=\begin{bmatrix} -1 & 2 & -2 \\4 & -3 & 4 \\4 & -4 & 5 \end{bmatrix}$ show that $A=A^{-1}$

asked Mar 29, 2013 by poojasapani_1

1 answer

If $A=\Large\frac{1}{3}$$\begin{bmatrix} 2 & 2 & 1 \\-2 & 1 & 2 \\1 & -2 & 2 \end{bmatrix}$ prove that $A^{-1}=A^T$.

asked Mar 29, 2013 by poojasapani_1

1 answer

Show that the adjoint of $A=\begin{bmatrix} -4 & -3 & -3 \\1 & 0 & 1 \\4 & 4 & 3 \end{bmatrix}$ is$\;A\;$ it self

asked Mar 28, 2013 by poojasapani_1

1 answer

Show that the adjoint of $A=\begin{bmatrix} -1 & -2 & -2 \\2 & 1 & -2 \\2 & -2 & 1 \end{bmatrix}$ is$\; 3A^T.$

asked Mar 28, 2013 by poojasapani_1

1 answer

If$A=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}$and$B=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix}$ verify that$(AB)^{T}=B^{T}A^{T}$

asked Mar 28, 2013 by poojasapani_1

1 answer

Find the inverse of the matrix $A=\begin{bmatrix} 3 & -3 & 4 \\2 & -3 & 4 \\0 & -1 & 1 \end{bmatrix}$ and verify that $A^3=A^{-1}$

asked Mar 28, 2013 by poojasapani_1

1 answer

If$A=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}$ and$B=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix}$ verify that $(AB)^{-1}=B^{-1}A^{-1}$

asked Mar 28, 2013 by poojasapani_1

1 answer

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

asked Mar 14, 2013 by meena.p

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:(iv) $f : N\to N\; 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 : R\to R $ given by $ f(x)\; = x^2 $

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

For any square matrix verify A(adj A) = |A|I

asked Jan 24, 2013 by meena.p

0 answers

If $ A=\begin{bmatrix} a & b \\ 0 & 1 \end{bmatrix}\;prove\;that\;A^n=\begin{bmatrix} \Large a^n & \Large\frac{b(a^n-1)}{a-1} \\ \normalsize 0 & 1 \end{bmatrix},n \epsilon N$

asked Jan 24, 2013 by meena.p

0 answers

Let $\begin{vmatrix} 3 & y \\ x & 1 \end{vmatrix} =\begin{vmatrix} 3 & 2 \\ 4 & 1 \end{vmatrix} $ find the possible values of x and y, find the values if x = y.

asked Jan 24, 2013 by meena.p

0 answers

If the points (2,0), (0,5) and (x,y) are collinear give a relation between x and y.

asked Jan 24, 2013 by meena.p

0 answers

If P and Q are invertible matrices of same order, then show that PQ is also invertible.

asked Jan 24, 2013 by meena.p

0 answers

Find x, if $ \begin{bmatrix} x & -5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} =0$

asked Jan 24, 2013 by meena.p

0 answers

If $ A=\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix} \;find\;A^2\;Hence\;find\;A^6.$

asked Jan 24, 2013 by meena.p

0 answers

If $A=\begin{bmatrix} \cos \theta & \sin \theta & \\ -\sin \theta & \cos \theta \end{bmatrix} $ then show that $A^n=\begin{bmatrix} \cos 2\theta & \sin 2\theta & \\ -\sin 2\theta & \cos 2\theta \end{bmatrix} $

asked Jan 24, 2013 by meena.p

0 answers

If a, b, c are in A.P. then find the value of: $\begin{vmatrix} 2y+4 & 5y+7 & 8y+a \\ 3y+5 & 6y+8 & 9y+b \\ 4y+6 & 7y+9 & 10y+c \end{vmatrix}$

asked Jan 24, 2013 by meena.p

0 answers

Prove that the Greatest Integer Function $f : R \to R$, given by $f (x) = [x]$, is neither one-one nor onto, where $[x]$ denotes the greatest integer less than or equal to $x$.

asked Nov 8, 2012 by vaishali.a

1 answer

Check the injectivity and surjectivity of the function: $f : N\to N\; given\; by\; f(x)\; = x^2 $

asked Nov 8, 2012 by vaishali.a

1 answer

Show that the function $f : R_* \rightarrow R_* $ defined by $ f(x) = (\frac{1} {x})$ is one-one and onto, where $R_* $ is the set of all non-zero real numbers. Is the result true, if the domain $R_* $ is replaced by $N$ with co-domain being same as $R_*$?

asked Nov 8, 2012 by vaishali.a

1 answer

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Gravel is being dumped from a conveyor belt at a rate of $30\;ft^{3}/min$ and its coarsened such that it forms a pile in the shape of the cone whose base diameter and hight are always equal. How fast is the hight of the pile increasing when the pile is $10$ ft hight?

For $A=\begin{bmatrix} -1 & 2 & -2 \\4 & -3 & 4 \\4 & -4 & 5 \end{bmatrix}$ show that $A=A^{-1}$

If $A=\Large\frac{1}{3}$$\begin{bmatrix} 2 & 2 & 1 \\-2 & 1 & 2 \\1 & -2 & 2 \end{bmatrix}$ prove that $A^{-1}=A^T$.

Show that the adjoint of $A=\begin{bmatrix} -4 & -3 & -3 \\1 & 0 & 1 \\4 & 4 & 3 \end{bmatrix}$ is$\;A\;$ it self

Show that the adjoint of $A=\begin{bmatrix} -1 & -2 & -2 \\2 & 1 & -2 \\2 & -2 & 1 \end{bmatrix}$ is$\; 3A^T.$

If$A=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}$and$B=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix}$ verify that\((AB)^{T}=B^{T}A^{T}\)

Find the inverse of the matrix $A=\begin{bmatrix} 3 & -3 & 4 \\2 & -3 & 4 \\0 & -1 & 1 \end{bmatrix}$ and verify that $A^3=A^{-1}$

If$A=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}$ and$B=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix}$ verify that \((AB)^{-1}=B^{-1}A^{-1}\)

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

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

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

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

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

For any square matrix verify A(adj A) = |A|I

If $ A=\begin{bmatrix} a & b \\ 0 & 1 \end{bmatrix}\;prove\;that\;A^n=\begin{bmatrix} \Large a^n & \Large\frac{b(a^n-1)}{a-1} \\ \normalsize 0 & 1 \end{bmatrix},n \epsilon N$

Let $\begin{vmatrix} 3 & y \\ x & 1 \end{vmatrix} =\begin{vmatrix} 3 & 2 \\ 4 & 1 \end{vmatrix} $ find the possible values of x and y, find the values if x = y.

If the points (2,0), (0,5) and (x,y) are collinear give a relation between x and y.

If P and Q are invertible matrices of same order, then show that PQ is also invertible.

Find x, if $ \begin{bmatrix} x & -5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} =0$

If $ A=\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix} \;find\;A^2\;Hence\;find\;A^6.$

If $A=\begin{bmatrix} \cos \theta & \sin \theta & \\ -\sin \theta & \cos \theta \end{bmatrix} $ then show that $A^n=\begin{bmatrix} \cos 2\theta & \sin 2\theta & \\ -\sin 2\theta & \cos 2\theta \end{bmatrix} $

If a, b, c are in A.P. then find the value of: $\begin{vmatrix} 2y+4 & 5y+7 & 8y+a \\ 3y+5 & 6y+8 & 9y+b \\ 4y+6 & 7y+9 & 10y+c \end{vmatrix}$

Prove that the Greatest Integer Function \(f : R \to R\), given by \(f (x) = [x]\), is neither one-one nor onto, where \([x]\) denotes the greatest integer less than or equal to \(x\).

Check the injectivity and surjectivity of the function: $f : N\to N\; given\; by\; f(x)\; = x^2 $

Show that the function \(f : R_* \rightarrow R_* \) defined by \( f(x) = (\frac{1} {x})\) is one-one and onto, where \(R_* \) is the set of all non-zero real numbers. Is the result true, if the domain \(R_* \) is replaced by \(N\) with co-domain being same as \(R_*\)?