Determinants and their Properties
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Matrix and Determinant

79080 If each element of a \(3 \times 3\) matrix is multiplied by 3 , then the determinant of the newly formed matrix is

1 \(3|\mathrm{~A}|\)
2 \(9|\mathrm{~A}|\)
3 \(27 \mid \mathrm{A}\)
4 \(|\mathrm{A}|^{3}\)
Rajasthan PET-2010
Matrix and Determinant

79081 IF \(\mathbf{A}+\mathbf{B}+\mathbf{C}=\pi\), then
\(\left|\begin{array}{ccc}\sin (A+B+C) & \sin B & \cos C \\ -\sin B & 0 & \tan A \\ \cos (A+B) & -\tan A & 0\end{array}\right|\) is equal to

1 \(\sin A\)
2 \(\sin A \cos B\)
3 0
4 None of these
Manipal-2018
Matrix and Determinant

79082 The value of \(\left|\begin{array}{ccc}a & a+b & a+2 b \\ a+2 b & a & a+b \\ a+b & a+2 b & a\end{array}\right|\) is equal to

1 \(9 a^{2}(a+b)\)
2 \(9 b^{2}(a+b)\)
3 \(a^{2}(a+b)\)
4 \(b^{2}(a+b)\)
Manipal-2018
Matrix and Determinant

79083 \(\left|\begin{array}{ccc}a^{2}+1 & a b & a c \\ a b & b^{2}+1 & b c \\ a c & c b & c^{2}+1\end{array}\right|=\)

1 \(1+b^{2}+c^{2}\)
2 \(a^{2}+b^{2}+c^{2}\)
3 \(1+a^{2}+b^{2}\)
4 \(1+a^{2}+b^{2}+c^{2}\)
Assam CEE-2022
Matrix and Determinant

79084 If \(a+b+c=0\), then \(a\) root of
\(\left|\begin{array}{ccc} \mathbf{a}-\mathbf{x} & \mathbf{c} & \mathbf{b} \\ \mathbf{c} & \mathbf{b}-\mathbf{x} & \mathbf{a} \\ \mathbf{b} & \mathbf{a} & \mathbf{c}-\mathbf{x} \end{array}\right|=\mathbf{0} \text { is }\)

1 0
2 1
3 \(\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}\)
4 3
Assam CEE-2022
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Matrix and Determinant

79080 If each element of a \(3 \times 3\) matrix is multiplied by 3 , then the determinant of the newly formed matrix is

1 \(3|\mathrm{~A}|\)
2 \(9|\mathrm{~A}|\)
3 \(27 \mid \mathrm{A}\)
4 \(|\mathrm{A}|^{3}\)
Rajasthan PET-2010
Matrix and Determinant

79081 IF \(\mathbf{A}+\mathbf{B}+\mathbf{C}=\pi\), then
\(\left|\begin{array}{ccc}\sin (A+B+C) & \sin B & \cos C \\ -\sin B & 0 & \tan A \\ \cos (A+B) & -\tan A & 0\end{array}\right|\) is equal to

1 \(\sin A\)
2 \(\sin A \cos B\)
3 0
4 None of these
Manipal-2018
Matrix and Determinant

79082 The value of \(\left|\begin{array}{ccc}a & a+b & a+2 b \\ a+2 b & a & a+b \\ a+b & a+2 b & a\end{array}\right|\) is equal to

1 \(9 a^{2}(a+b)\)
2 \(9 b^{2}(a+b)\)
3 \(a^{2}(a+b)\)
4 \(b^{2}(a+b)\)
Manipal-2018
Matrix and Determinant

79083 \(\left|\begin{array}{ccc}a^{2}+1 & a b & a c \\ a b & b^{2}+1 & b c \\ a c & c b & c^{2}+1\end{array}\right|=\)

1 \(1+b^{2}+c^{2}\)
2 \(a^{2}+b^{2}+c^{2}\)
3 \(1+a^{2}+b^{2}\)
4 \(1+a^{2}+b^{2}+c^{2}\)
Assam CEE-2022
Matrix and Determinant

79084 If \(a+b+c=0\), then \(a\) root of
\(\left|\begin{array}{ccc} \mathbf{a}-\mathbf{x} & \mathbf{c} & \mathbf{b} \\ \mathbf{c} & \mathbf{b}-\mathbf{x} & \mathbf{a} \\ \mathbf{b} & \mathbf{a} & \mathbf{c}-\mathbf{x} \end{array}\right|=\mathbf{0} \text { is }\)

1 0
2 1
3 \(\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}\)
4 3
Assam CEE-2022
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Matrix and Determinant

79080 If each element of a \(3 \times 3\) matrix is multiplied by 3 , then the determinant of the newly formed matrix is

1 \(3|\mathrm{~A}|\)
2 \(9|\mathrm{~A}|\)
3 \(27 \mid \mathrm{A}\)
4 \(|\mathrm{A}|^{3}\)
Rajasthan PET-2010
Matrix and Determinant

79081 IF \(\mathbf{A}+\mathbf{B}+\mathbf{C}=\pi\), then
\(\left|\begin{array}{ccc}\sin (A+B+C) & \sin B & \cos C \\ -\sin B & 0 & \tan A \\ \cos (A+B) & -\tan A & 0\end{array}\right|\) is equal to

1 \(\sin A\)
2 \(\sin A \cos B\)
3 0
4 None of these
Manipal-2018
Matrix and Determinant

79082 The value of \(\left|\begin{array}{ccc}a & a+b & a+2 b \\ a+2 b & a & a+b \\ a+b & a+2 b & a\end{array}\right|\) is equal to

1 \(9 a^{2}(a+b)\)
2 \(9 b^{2}(a+b)\)
3 \(a^{2}(a+b)\)
4 \(b^{2}(a+b)\)
Manipal-2018
Matrix and Determinant

79083 \(\left|\begin{array}{ccc}a^{2}+1 & a b & a c \\ a b & b^{2}+1 & b c \\ a c & c b & c^{2}+1\end{array}\right|=\)

1 \(1+b^{2}+c^{2}\)
2 \(a^{2}+b^{2}+c^{2}\)
3 \(1+a^{2}+b^{2}\)
4 \(1+a^{2}+b^{2}+c^{2}\)
Assam CEE-2022
Matrix and Determinant

79084 If \(a+b+c=0\), then \(a\) root of
\(\left|\begin{array}{ccc} \mathbf{a}-\mathbf{x} & \mathbf{c} & \mathbf{b} \\ \mathbf{c} & \mathbf{b}-\mathbf{x} & \mathbf{a} \\ \mathbf{b} & \mathbf{a} & \mathbf{c}-\mathbf{x} \end{array}\right|=\mathbf{0} \text { is }\)

1 0
2 1
3 \(\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}\)
4 3
Assam CEE-2022
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Matrix and Determinant

79080 If each element of a \(3 \times 3\) matrix is multiplied by 3 , then the determinant of the newly formed matrix is

1 \(3|\mathrm{~A}|\)
2 \(9|\mathrm{~A}|\)
3 \(27 \mid \mathrm{A}\)
4 \(|\mathrm{A}|^{3}\)
Rajasthan PET-2010
Matrix and Determinant

79081 IF \(\mathbf{A}+\mathbf{B}+\mathbf{C}=\pi\), then
\(\left|\begin{array}{ccc}\sin (A+B+C) & \sin B & \cos C \\ -\sin B & 0 & \tan A \\ \cos (A+B) & -\tan A & 0\end{array}\right|\) is equal to

1 \(\sin A\)
2 \(\sin A \cos B\)
3 0
4 None of these
Manipal-2018
Matrix and Determinant

79082 The value of \(\left|\begin{array}{ccc}a & a+b & a+2 b \\ a+2 b & a & a+b \\ a+b & a+2 b & a\end{array}\right|\) is equal to

1 \(9 a^{2}(a+b)\)
2 \(9 b^{2}(a+b)\)
3 \(a^{2}(a+b)\)
4 \(b^{2}(a+b)\)
Manipal-2018
Matrix and Determinant

79083 \(\left|\begin{array}{ccc}a^{2}+1 & a b & a c \\ a b & b^{2}+1 & b c \\ a c & c b & c^{2}+1\end{array}\right|=\)

1 \(1+b^{2}+c^{2}\)
2 \(a^{2}+b^{2}+c^{2}\)
3 \(1+a^{2}+b^{2}\)
4 \(1+a^{2}+b^{2}+c^{2}\)
Assam CEE-2022
Matrix and Determinant

79084 If \(a+b+c=0\), then \(a\) root of
\(\left|\begin{array}{ccc} \mathbf{a}-\mathbf{x} & \mathbf{c} & \mathbf{b} \\ \mathbf{c} & \mathbf{b}-\mathbf{x} & \mathbf{a} \\ \mathbf{b} & \mathbf{a} & \mathbf{c}-\mathbf{x} \end{array}\right|=\mathbf{0} \text { is }\)

1 0
2 1
3 \(\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}\)
4 3
Assam CEE-2022
Join With Us for More Updates
Matrix and Determinant

79080 If each element of a \(3 \times 3\) matrix is multiplied by 3 , then the determinant of the newly formed matrix is

1 \(3|\mathrm{~A}|\)
2 \(9|\mathrm{~A}|\)
3 \(27 \mid \mathrm{A}\)
4 \(|\mathrm{A}|^{3}\)
Rajasthan PET-2010
Matrix and Determinant

79081 IF \(\mathbf{A}+\mathbf{B}+\mathbf{C}=\pi\), then
\(\left|\begin{array}{ccc}\sin (A+B+C) & \sin B & \cos C \\ -\sin B & 0 & \tan A \\ \cos (A+B) & -\tan A & 0\end{array}\right|\) is equal to

1 \(\sin A\)
2 \(\sin A \cos B\)
3 0
4 None of these
Manipal-2018
Matrix and Determinant

79082 The value of \(\left|\begin{array}{ccc}a & a+b & a+2 b \\ a+2 b & a & a+b \\ a+b & a+2 b & a\end{array}\right|\) is equal to

1 \(9 a^{2}(a+b)\)
2 \(9 b^{2}(a+b)\)
3 \(a^{2}(a+b)\)
4 \(b^{2}(a+b)\)
Manipal-2018
Matrix and Determinant

79083 \(\left|\begin{array}{ccc}a^{2}+1 & a b & a c \\ a b & b^{2}+1 & b c \\ a c & c b & c^{2}+1\end{array}\right|=\)

1 \(1+b^{2}+c^{2}\)
2 \(a^{2}+b^{2}+c^{2}\)
3 \(1+a^{2}+b^{2}\)
4 \(1+a^{2}+b^{2}+c^{2}\)
Assam CEE-2022
Matrix and Determinant

79084 If \(a+b+c=0\), then \(a\) root of
\(\left|\begin{array}{ccc} \mathbf{a}-\mathbf{x} & \mathbf{c} & \mathbf{b} \\ \mathbf{c} & \mathbf{b}-\mathbf{x} & \mathbf{a} \\ \mathbf{b} & \mathbf{a} & \mathbf{c}-\mathbf{x} \end{array}\right|=\mathbf{0} \text { is }\)

1 0
2 1
3 \(\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}\)
4 3
Assam CEE-2022