Determinants and their Properties
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Matrix and Determinant

79041 If \(z_{1}=\mathbf{2}+3 i, z_{2}=\mathbf{3}+2 \mathbf{i}\) where \(i=\sqrt{-1}\) then \(\left[\begin{array}{cc}\mathrm{z}_{1} & \mathrm{z}_{2} \\ \overline{\mathrm{z}}_{2} & \overline{\mathrm{Z}}_{1}\end{array}\right]\left[\begin{array}{cc}\overline{\mathrm{Z}}_{1} & -\mathrm{z}_{2} \\ \overline{\mathrm{z}}_{2} & \mathrm{z}_{1}\end{array}\right]=\)

1 \(13 \mathrm{I}\)
2 I
3 \(26 \mathrm{I}\)
4 Zero matrix
Shift-II]
Matrix and Determinant

79042 What is the value of \(\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|=\) ?

1 \(\mathrm{a}^{3}+\mathrm{b}^{3}+\mathrm{c}^{3}+3 \mathrm{abc}\)
2 \(a^{3}+b^{3}+c^{3}-3 a b c\)
3 \(a^{3}+b^{3}+c^{3}-6 a b c\)
4 \(a^{3}+b^{3}+c^{3}+6 a b c\)
Shift-II]
Matrix and Determinant

79043 Let \(a \in\) and \(A=\left[\begin{array}{ccc}a & a & a-y \\ a & a+x & a \\ a & a & a\end{array}\right]\) be a matrix.
Then equation \(\operatorname{det} A=16\)

1 a parabola
2 a circle
3 an ellipse
4 a rectangular hyperbola
Shift-II]
Matrix and Determinant

79046 The number of positive roots of the equation
\(\left|\begin{array}{lll}\mathbf{x} & 3 & 7 \\ 2 & \mathbf{x} & \mathbf{2} \\ 7 & \mathbf{6} & \mathbf{x}\end{array}\right|=\mathbf{0}\) is :

1 1
2 2
3 3
4 0
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Matrix and Determinant

79041 If \(z_{1}=\mathbf{2}+3 i, z_{2}=\mathbf{3}+2 \mathbf{i}\) where \(i=\sqrt{-1}\) then \(\left[\begin{array}{cc}\mathrm{z}_{1} & \mathrm{z}_{2} \\ \overline{\mathrm{z}}_{2} & \overline{\mathrm{Z}}_{1}\end{array}\right]\left[\begin{array}{cc}\overline{\mathrm{Z}}_{1} & -\mathrm{z}_{2} \\ \overline{\mathrm{z}}_{2} & \mathrm{z}_{1}\end{array}\right]=\)

1 \(13 \mathrm{I}\)
2 I
3 \(26 \mathrm{I}\)
4 Zero matrix
Shift-II]
Matrix and Determinant

79042 What is the value of \(\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|=\) ?

1 \(\mathrm{a}^{3}+\mathrm{b}^{3}+\mathrm{c}^{3}+3 \mathrm{abc}\)
2 \(a^{3}+b^{3}+c^{3}-3 a b c\)
3 \(a^{3}+b^{3}+c^{3}-6 a b c\)
4 \(a^{3}+b^{3}+c^{3}+6 a b c\)
Shift-II]
Matrix and Determinant

79043 Let \(a \in\) and \(A=\left[\begin{array}{ccc}a & a & a-y \\ a & a+x & a \\ a & a & a\end{array}\right]\) be a matrix.
Then equation \(\operatorname{det} A=16\)

1 a parabola
2 a circle
3 an ellipse
4 a rectangular hyperbola
Shift-II]
Matrix and Determinant

79046 The number of positive roots of the equation
\(\left|\begin{array}{lll}\mathbf{x} & 3 & 7 \\ 2 & \mathbf{x} & \mathbf{2} \\ 7 & \mathbf{6} & \mathbf{x}\end{array}\right|=\mathbf{0}\) is :

1 1
2 2
3 3
4 0
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Matrix and Determinant

79041 If \(z_{1}=\mathbf{2}+3 i, z_{2}=\mathbf{3}+2 \mathbf{i}\) where \(i=\sqrt{-1}\) then \(\left[\begin{array}{cc}\mathrm{z}_{1} & \mathrm{z}_{2} \\ \overline{\mathrm{z}}_{2} & \overline{\mathrm{Z}}_{1}\end{array}\right]\left[\begin{array}{cc}\overline{\mathrm{Z}}_{1} & -\mathrm{z}_{2} \\ \overline{\mathrm{z}}_{2} & \mathrm{z}_{1}\end{array}\right]=\)

1 \(13 \mathrm{I}\)
2 I
3 \(26 \mathrm{I}\)
4 Zero matrix
Shift-II]
Matrix and Determinant

79042 What is the value of \(\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|=\) ?

1 \(\mathrm{a}^{3}+\mathrm{b}^{3}+\mathrm{c}^{3}+3 \mathrm{abc}\)
2 \(a^{3}+b^{3}+c^{3}-3 a b c\)
3 \(a^{3}+b^{3}+c^{3}-6 a b c\)
4 \(a^{3}+b^{3}+c^{3}+6 a b c\)
Shift-II]
Matrix and Determinant

79043 Let \(a \in\) and \(A=\left[\begin{array}{ccc}a & a & a-y \\ a & a+x & a \\ a & a & a\end{array}\right]\) be a matrix.
Then equation \(\operatorname{det} A=16\)

1 a parabola
2 a circle
3 an ellipse
4 a rectangular hyperbola
Shift-II]
Matrix and Determinant

79046 The number of positive roots of the equation
\(\left|\begin{array}{lll}\mathbf{x} & 3 & 7 \\ 2 & \mathbf{x} & \mathbf{2} \\ 7 & \mathbf{6} & \mathbf{x}\end{array}\right|=\mathbf{0}\) is :

1 1
2 2
3 3
4 0
For More Updates join with Us
Matrix and Determinant

79041 If \(z_{1}=\mathbf{2}+3 i, z_{2}=\mathbf{3}+2 \mathbf{i}\) where \(i=\sqrt{-1}\) then \(\left[\begin{array}{cc}\mathrm{z}_{1} & \mathrm{z}_{2} \\ \overline{\mathrm{z}}_{2} & \overline{\mathrm{Z}}_{1}\end{array}\right]\left[\begin{array}{cc}\overline{\mathrm{Z}}_{1} & -\mathrm{z}_{2} \\ \overline{\mathrm{z}}_{2} & \mathrm{z}_{1}\end{array}\right]=\)

1 \(13 \mathrm{I}\)
2 I
3 \(26 \mathrm{I}\)
4 Zero matrix
Shift-II]
Matrix and Determinant

79042 What is the value of \(\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|=\) ?

1 \(\mathrm{a}^{3}+\mathrm{b}^{3}+\mathrm{c}^{3}+3 \mathrm{abc}\)
2 \(a^{3}+b^{3}+c^{3}-3 a b c\)
3 \(a^{3}+b^{3}+c^{3}-6 a b c\)
4 \(a^{3}+b^{3}+c^{3}+6 a b c\)
Shift-II]
Matrix and Determinant

79043 Let \(a \in\) and \(A=\left[\begin{array}{ccc}a & a & a-y \\ a & a+x & a \\ a & a & a\end{array}\right]\) be a matrix.
Then equation \(\operatorname{det} A=16\)

1 a parabola
2 a circle
3 an ellipse
4 a rectangular hyperbola
Shift-II]
Matrix and Determinant

79046 The number of positive roots of the equation
\(\left|\begin{array}{lll}\mathbf{x} & 3 & 7 \\ 2 & \mathbf{x} & \mathbf{2} \\ 7 & \mathbf{6} & \mathbf{x}\end{array}\right|=\mathbf{0}\) is :

1 1
2 2
3 3
4 0
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