Classes

First Year Math Matrices and Determinants


Change the way you learn with Maqsad's classes. Local examples, engaging animations, and instant video solutions keep you on your toes and make learning fun like never before!

Class 9Class 10First YearSecond Year
Evaluatethefollowingdeterminantsusingtheirproperties.8.xyzzxyyzxEvaluate the following determinants using their properties.8. \left|\begin{array}{lll}x & y & z \\ z & x & y \\ y & z & x\end{array}\right|

Q.20 If A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] then adj A equals :(a) \left[\begin{array}{rr}d & b \\ -c & a\end{array}\right] (b) \left[\begin{array}{rr}d & -b \\ -c & a\end{array}\right] (c) \left[\begin{array}{ll}d & b \\ c & a\end{array}\right] (d) \left[\begin{array}{rr}d & -b \\ c & a\end{array}\right] Gujranwala Board 2007
Q.20 If  A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]  then adj  A  equals :(a)  \left[\begin{array}{rr}d & b \\ -c & a\end{array}\right] (b)  \left[\begin{array}{rr}d & -b \\ -c & a\end{array}\right] (c)  \left[\begin{array}{ll}d & b \\ c & a\end{array}\right] (d)  \left[\begin{array}{rr}d & -b \\ c & a\end{array}\right] Gujranwala Board 2007

Q.20IfA=[abcd]thenadjAequals:(a)[dbca](b)[dbca](c)[dbca](d)[dbca]GujranwalaBoard2007Q.20 If A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] then adj A equals :(a) \left[\begin{array}{rr}d & b \\ -c & a\end{array}\right] (b) \left[\begin{array}{rr}d & -b \\ -c & a\end{array}\right] (c) \left[\begin{array}{ll}d & b \\ c & a\end{array}\right] (d) \left[\begin{array}{rr}d & -b \\ c & a\end{array}\right] Gujranwala Board 2007

Evaluate the following determinants using their properties.8. \left|\begin{array}{lll}x & y & z \\ z & x & y \\ y & z & x\end{array}\right|
Evaluate the following determinants using their properties.8.  \left|\begin{array}{lll}x & y & z \\ z & x & y \\ y & z & x\end{array}\right|
now playing

Evaluatethefollowingdeterminantsusingtheirproperties.8.xyzzxyyzxEvaluate the following determinants using their properties.8. \left|\begin{array}{lll}x & y & z \\ z & x & y \\ y & z & x\end{array}\right|

Evaluate the following determinants:6. \left|\begin{array}{lll}1 & 1 & \omega \\ 1 & 1 & \omega^{2} \\ \omega & \omega^{2} & 1\end{array}\right| where \omega is a complex cube root of unity.
Evaluate the following determinants:6.  \left|\begin{array}{lll}1 & 1 & \omega \\ 1 & 1 & \omega^{2} \\ \omega & \omega^{2} & 1\end{array}\right| where  \omega  is a complex cube root of unity.

Evaluatethefollowingdeterminants:6.11ω11ω2ωω21whereωisacomplexcuberootofunity.Evaluate the following determinants:6. \left|\begin{array}{lll}1 & 1 & \omega \\ 1 & 1 & \omega^{2} \\ \omega & \omega^{2} & 1\end{array}\right| where \omega is a complex cube root of unity.

17. Let \mathrm{A}=\left[\begin{array}{ccc}1 & 3 & 0 \\ -1 & 2 & 1 \\ 0 & 0 & 2\end{array}\right] \mathrm{B}=\left[\begin{array}{ccc}2 & 3 & 4 \\ 1 & 2 & 3 \\ -1 & 1 & 2\end{array}\right] and C=\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 5 & 8 \\ 2 & 7 & 6\end{array}\right] Show that :(V) \mathrm{A}+\mathrm{B}=\mathrm{B}+\mathrm{A}^{-7}=\pm=
17. Let  \mathrm{A}=\left[\begin{array}{ccc}1 & 3 & 0 \\ -1 & 2 & 1 \\ 0 & 0 & 2\end{array}\right] \mathrm{B}=\left[\begin{array}{ccc}2 & 3 & 4 \\ 1 & 2 & 3 \\ -1 & 1 & 2\end{array}\right]  and  C=\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 5 & 8 \\ 2 & 7 & 6\end{array}\right] Show that :(V)  \mathrm{A}+\mathrm{B}=\mathrm{B}+\mathrm{A}^{-7}=\pm=

17.LetA=[130121002]B=[234123112]andC=[123358276]Showthat:(V)A+B=B+A7=±=17. Let \mathrm{A}=\left[\begin{array}{ccc}1 & 3 & 0 \\ -1 & 2 & 1 \\ 0 & 0 & 2\end{array}\right] \mathrm{B}=\left[\begin{array}{ccc}2 & 3 & 4 \\ 1 & 2 & 3 \\ -1 & 1 & 2\end{array}\right] and C=\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 5 & 8 \\ 2 & 7 & 6\end{array}\right] Show that :(V) \mathrm{A}+\mathrm{B}=\mathrm{B}+\mathrm{A}^{-7}=\pm=

(vi) Product of \left[\begin{array}{ll}x & y\end{array}\right]\left[\begin{array}{c}2 \\ -1\end{array}\right] is(a) [2 x+y] (b) [x-2 y] (c) [2 x-y] (d) [x+2 y]
(vi) Product of  \left[\begin{array}{ll}x & y\end{array}\right]\left[\begin{array}{c}2 \\ -1\end{array}\right]  is(a)  [2 x+y] (b)  [x-2 y] (c)  [2 x-y] (d)  [x+2 y]

(vi)Productof[xy][21]is(a)[2x+y](b)[x2y](c)[2xy](d)[x+2y](vi) Product of \left[\begin{array}{ll}x & y\end{array}\right]\left[\begin{array}{c}2 \\ -1\end{array}\right] is(a) [2 x+y] (b) [x-2 y] (c) [2 x-y] (d) [x+2 y]

Q.14 \left[\begin{array}{lll}0 & 0 & 0\end{array}\right] is(a) scalar matrix(b) diagonal matrix(c) identity matrix(d) null matrix
Q.14  \left[\begin{array}{lll}0 & 0 & 0\end{array}\right]  is(a) scalar matrix(b) diagonal matrix(c) identity matrix(d) null matrix

Q.14[000]is(a)scalarmatrix(b)diagonalmatrix(c)identitymatrix(d)nullmatrixQ.14 \left[\begin{array}{lll}0 & 0 & 0\end{array}\right] is(a) scalar matrix(b) diagonal matrix(c) identity matrix(d) null matrix

banner6000+ MCQs with instant video solutions