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First Year Math Matrices and Determinants


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Class 9Class 10First YearSecond Year
Q.36IfA=[1764]thenAisequalto:(a)46(b)46(c)38(d)38Q.36 If A=\left[\begin{array}{ll}1 & 7 \\ 6 & 4\end{array}\right] then |A| is equal to :(a) 46(b) -46 (c) 38(d) -38

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|

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

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