Email

Chat with tutors

Login

Ask Questions, Get Answers

Menu X

home ask tuition questions practice papers mobile tutors pricing

X

Recent questions tagged ch4

If $A=\begin{bmatrix}1 & 2 & 0\\-2 & -1 & -2\\0 & -1 & 1\end{bmatrix},find\;A^{-1}.$\[Using\;A^{-1}, solve\; the\; system\; of\; linear\; equations\; x-2y=10,2x-y-z=8,-2y+Z=7.\]

asked Dec 26, 2012 by sreemathi.v

1 answer

Find $A^{-1}$ if $A=\begin{bmatrix}0 & 1 & 1\\1 & 0 & 1\\1 & 1 & 0\end{bmatrix}$ and show that $ A^{-1}=\Large \frac{A^2-3I}{2}$

asked Dec 26, 2012 by sreemathi.v

1 answer

show that the $\Delta$ABC is an isosceles triangle if the determinant\[\Delta=\begin{bmatrix}1 & 1& 1\\1+\cos A & 1+\cos B & 1+\cos C\\\cos^2A+\cos A & \cos^2B+\cos B & \cos^2C+\cos C\end{bmatrix}=0\]

asked Dec 26, 2012 by sreemathi.v

1 answer

Using properties of determinants, prove that : $ \begin{bmatrix} a^2+1 & ab & ac \\ ab & b^2+1 & bc \\ ca & cb & c^2+1 \end{bmatrix} = (1+a^2+b^2+c^2) $

asked Dec 26, 2012 by thanvigandhi_1

0 answers

Show that the point(a+5,a-4),(a-2,a+3) and (a,a) do not lie on a straight line for any value of a.

asked Dec 24, 2012 by sreemathi.v

1 answer

If $a_1,a_2,a_3,....,a_r$ are in G.P., then prove that the determinant $\begin{vmatrix} a_{r-1} & a_{r-5} & a_{r-9} \\ a_{r-7} & a_{r-11} & a_{r-15} \\ a_{r-13} & a_{r-17} & a_{r-21} \end{vmatrix} is\; independent\; of\; r$

asked Dec 24, 2012 by sreemathi.v

1 answer

Find the value of $\theta$ satisfying $\begin{bmatrix} 1 & 1 & \sin3\theta \\ -4 & 3 & \cos2\theta \\ 7 & -7 & -2 \end{bmatrix}\;=\;0$

asked Dec 24, 2012 by sreemathi.v

1 answer

Using the properties of determinants, Prove that$\begin{vmatrix} y+z & z & y \\ z & z+x & x \\ y & x & x+y \end{vmatrix}\;=\;4xyz$

asked Dec 24, 2012 by sreemathi.v

1 answer

Using the properties of determinants, prove that: $\begin{vmatrix} y^2z^2 & yz &y+ z \\ z^2x^2 & zx & z+x \\ x^2y^2 & xy & x+y \end{vmatrix}\;=\;0$

asked Dec 24, 2012 by sreemathi.v

1 answer

Using the properties of determinants, evaluate $\begin{vmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{vmatrix}$

asked Dec 24, 2012 by sreemathi.v

1 answer

Using the properties of determinants, evaluate $\begin{vmatrix} x+4 & x & x \\ x & x+4 & x \\ x & x & x+4 \end{vmatrix}$

asked Dec 24, 2012 by sreemathi.v

1 answer

Using the properties of determinants, evaluate $\begin{vmatrix} 3x & -x+y & -x+z \\ x-y & 3y & z-y \\ x-z & y-z & 3z \end{vmatrix}$

asked Dec 24, 2012 by sreemathi.v

1 answer

Using the properties of determinants, evaluate $\begin{vmatrix} 0 & xy^2 & xz^2 \\ x^2y & 0 & yz^2 \\ x^2z & zy^2 & 0 \end{vmatrix}$

asked Dec 24, 2012 by sreemathi.v

1 answer

Using the properties of determinants, evaluate $\begin{vmatrix} a+x & y & z \\ x & a+y & z \\ x & y & a+z \end{vmatrix}$

asked Dec 24, 2012 by sreemathi.v

1 answer

Using the properties of determinants, evaluate $\begin{vmatrix} x^2 - x+1 & x-1 \\ x +1 & x+1 \end{vmatrix}$

asked Dec 24, 2012 by sreemathi.v

1 answer

Let A = $\begin{bmatrix} 1 & sin\theta & 1 \\ -sin\theta & 1 & sin\theta \\ -1 & -sin\theta & 1 \end{bmatrix}$, where $0 \leq \theta \leq 2\pi$. Then: \[ \begin{array} ((A) \, Det(A) = 0 \quad& (B) \, Det(A) \in (2, \infty) \\[0.5em] (C) \, Det(A) \in (2, 4) \quad &(D) Det(A) \in [2,4] \end{array} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If x, y, z are nonzero real numbers, then the inverse of matrix A = $\begin{bmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{bmatrix}$ is

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Choose the correct answer. If a, b, c, are in A.P, then the determinant $\begin{vmatrix} x+2 & x+3 &x+2a \\ x+3 & x+4 &x+2b \\ x+4 & x+5 &x+2c \end{vmatrix}$ is: \[\] $(A)\;0 \hspace{20 mm} (B)\;1 \hspace{20 mm} (C)\; x \hspace{20 mm} (D)\; 2x $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the system of equations: $\large \frac{2}{x}+\frac{3}{y}+\frac{10}{z}=$$4.\quad $ $\large \frac{4}{x}-\frac{6}{y}+\frac{5}{z}$$=1.\quad $ $\large \frac{6}{x}+\frac{9}{y}-\frac{20}{z}$$=2.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} sin\alpha&cos\alpha&cos(\alpha+\delta)\\ sin\beta&cos\beta&cos(\beta+\delta)\\ sin\gamma&cos\gamma&cos(\gamma+\delta)) \end{vmatrix}= 0.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} 1&1+p&1+p+q\\ 2&3+2p&4+3p+2q\\ 3&6+3p&10+6p+3q \end{vmatrix}= 1.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} 3a&-a+b&-a+c\\ -b+a&3b&-b+c\\ -c+a&-c+b&3c \end{vmatrix}= 3(a+b+c)(ab+bc+ca)$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $ \begin{vmatrix} x &x^2 &1 & px^3\\ y &y^2 &1 & py^3\\ z &z^2 &1 & pz^3 \end{vmatrix}= (1+pxyz) (x-z) (y-z)(z-x), $ where p is any scalar.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} \alpha & \alpha^2 & \beta+\gamma\\ \beta & \beta^2 & \alpha+\gamma\\ \gamma & \gamma^2 & \alpha+\beta \end{vmatrix} = (\beta-\gamma) (\gamma - \alpha) (\alpha-\beta) (\alpha+\beta+\gamma)$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Evaluate $\begin{vmatrix} 1 & x & y\\ 1 & x+y & y\\ 1 & x & x+y \end{vmatrix}$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Evaluate $ \begin{vmatrix} x & y & x+y\\ y & x+y & x\\ x+y & x & y \end{vmatrix}$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Let A = $\begin{bmatrix} 1 & -2 & 1\\ -2 & 3 & 1\\ 1 & 1 & 5 \end{bmatrix}$. Verify that \[\] $(i)\ \; \left [adj A \right ]^{-1} = adj(A^{-1}) \;\;\;\; $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

$If \; A^{-1}=\begin{bmatrix} 3 &-1 & 1\\ -15&6 &-5 \\ 5& -2&2 \end{bmatrix} \; and \; B = \begin{bmatrix} 1 & 2 & -2\\ -1 & 3 & 0\\ 0 & -2 & 1 \end{bmatrix}, \; find \; (AB)^{-1} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Prove that $ \begin{vmatrix} a^2&bc&ac+c^2\\ a^2+ab& b^2& ac\\ ab&b^2+bc&c^2 \end{vmatrix}=4\,a^2\;b^2\;c^2. $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the equation $ \begin{vmatrix} x+a & x & x \\ x & x+a & x\\ x & x & x+a \end{vmatrix}=0, \; a \neq 0. $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If a, b and c are real numbers, and $\Delta = \begin{vmatrix} b+c & c+a & a+b \\ c+a & a+b & b+c\\ a+b & b+c & c+a \end{vmatrix}=0, $ show that either $a+b+c=0$ or $a=b=c.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Evaluate $ \begin{vmatrix} cos\alpha \; cos\beta & cos\alpha \; sin\beta & -sin\alpha \\ -sin\beta & cos\beta & 0 \\ sin \alpha \; cos\beta & sin\alpha \; sin\beta & cos\alpha \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Without expanding the determinant, prove that $ \begin{vmatrix} a &a^2 &bc \\ b &b^2 &ca \\ c &c^2 &ab \end{vmatrix}\; = \; \begin{vmatrix} 1 & a^2 & a^3 \\ 1 & b^2 & b^3 \\ 1 & c^2 & c^3 \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

\[ \text{Prove that the determinant } \begin{vmatrix} x&sin\theta&cos\theta \\ -sin\theta&-x&1\\ cos\theta&1&x \end{vmatrix} \text{ is independent of } \theta \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If $A = \begin{bmatrix} 2 &-3 & 5\\ 3& 2 & -4\\ 1& 1& -2 \end{bmatrix}$, $\;$ find $A^{-1}.\;$ Using $ A^{-1}$ solve the system of equations: \[2x-3y+5z=11\] \[3x+2y-4z = -5\] \[x+y-2z = -3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[x-y+2z=7\] \[3x+4y-5z=-5\] \[2x-y+3z=12\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[2x+3y+3z=5\] \[x-2y+z=-4\] \[3x-y-2z=3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[x-y+z=4\] \[2x+y-3z=0\] \[x+y+z=2\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[2x+y+z=1\] \[x-2y-z = \frac{3}{2}\] \[3y-5z=9\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:<br>$5x+2y=3$ <br> $3x+2y=5$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:<br>$4x-3y=3$ <br> $3x-5y=7$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:<br> $2x-y=-2$ <br> $3x+4y = 3$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method: <br>$5x+2y=4 $<br>$7x+3y = 5$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad 5x -y +4z = 5 \] \[\quad2x + 3y + 5z= 2\] \[\quad 5x - 2y + 6z = -1\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad 3x -y -2z = 2 \] \[\quad 2y -z = -1\] \[\quad 3x -5y = 3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad x + y + z = 1 \] \[\quad 2x + 3y +2z = 2\] \[\quad ax + ay +2az = 4\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad x + 3y = 5 \] \[\quad 2x + 6y = 8\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad 2x -y = 5 \] \[\quad x + y = 4\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad x + 2y = 2 \] \[\quad 2x + 3y = 3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Page:

« prev
1
...
20
21
22
23
24
25
next »

Feedback Terms Facebook Twitter About Us

Your payment for is successful.

...