Determinants and their Properties
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Matrix and Determinant

79047 Let \(A=\left(\begin{array}{cc}x+2 & 3 x \\ 3 & x+2\end{array}\right), B=\left(\begin{array}{cc}x & 0 \\ 5 & x+2\end{array}\right)\). Then all solutions of the equation \(\operatorname{det}(A B)=0\) is

1 \(1,-1,0,2\)
2 \(1,4,0,-2\)
3 \(1,-1,4,3\)
4 \(-1,4,0,3\)
WB JEE-2017
Matrix and Determinant

79048 The linear system of equations
\(\left.\begin{array}{r}
8 x-3 y-5 z=0 \\ 5 x-8 y+3 z=0 \\ 3 x+5 y-8 z=0 \end{array}\right\} \text { has }\)

1 only zero solution
2 only finite number of non-zero solutions
3 no non-zero solution
4 infinitely many non-zero solutions
WB JEE-2017
Matrix and Determinant

79049 The system of equations
\(\lambda x+y+3 z=0\)
\(2 x+\mu y-z=0\)
\(5 x+7 y+z=0\)
has infinitely many solutions in \(\mathrm{R}\). Then,

1 \(y=2, \mu=3\)
2 \(\lambda=1, \mu=2\)
3 \(\lambda=1, \mu=3\)
4 \(\lambda=3, \mu=1\)
WB JEE-2019
Matrix and Determinant

79050 Find the value of ' \(k\) ', if
\(\left|\begin{array}{lll}\mathrm{k}-2 & 2 \mathrm{k}-3 & 3 \mathrm{k}-4 \\ \mathrm{k}-4 & 2 \mathrm{k}-9 & 3 \mathrm{k}-16 \\ \mathrm{k}-8 & 2 \mathrm{k}-27 & 3 \mathrm{k}-64\end{array}\right|=0\)

1 1
2 2
3 3
4 4
Shift-I]
Matrix and Determinant

79051 For any \(a, b, c \in R\), the determinant
\(\left|\begin{array}{ccc}\mathbf{b c} & \mathbf{b}+\mathbf{c} & \mathbf{1} \\ \mathbf{c a} & \mathbf{c}+\mathbf{a} & \mathbf{1} \\ \mathbf{a b} & \mathbf{a}+\mathbf{b} & \mathbf{1}\end{array}\right|\) is equal to

1 \(a\left(b^{2}-c^{2}\right)+b\left(c^{2}-a^{2}\right)+c\left(a^{2}-b^{2}\right)\)
2 \(a(b-c)+b(c-a)+c(a-b)\)
3 \((a-b)(b-c)(c-a)\)
4 abc
AP EAMCET-2020-21.09.2020
Join With Us for More Updates
Matrix and Determinant

79047 Let \(A=\left(\begin{array}{cc}x+2 & 3 x \\ 3 & x+2\end{array}\right), B=\left(\begin{array}{cc}x & 0 \\ 5 & x+2\end{array}\right)\). Then all solutions of the equation \(\operatorname{det}(A B)=0\) is

1 \(1,-1,0,2\)
2 \(1,4,0,-2\)
3 \(1,-1,4,3\)
4 \(-1,4,0,3\)
WB JEE-2017
Matrix and Determinant

79048 The linear system of equations
\(\left.\begin{array}{r}
8 x-3 y-5 z=0 \\ 5 x-8 y+3 z=0 \\ 3 x+5 y-8 z=0 \end{array}\right\} \text { has }\)

1 only zero solution
2 only finite number of non-zero solutions
3 no non-zero solution
4 infinitely many non-zero solutions
WB JEE-2017
Matrix and Determinant

79049 The system of equations
\(\lambda x+y+3 z=0\)
\(2 x+\mu y-z=0\)
\(5 x+7 y+z=0\)
has infinitely many solutions in \(\mathrm{R}\). Then,

1 \(y=2, \mu=3\)
2 \(\lambda=1, \mu=2\)
3 \(\lambda=1, \mu=3\)
4 \(\lambda=3, \mu=1\)
WB JEE-2019
Matrix and Determinant

79050 Find the value of ' \(k\) ', if
\(\left|\begin{array}{lll}\mathrm{k}-2 & 2 \mathrm{k}-3 & 3 \mathrm{k}-4 \\ \mathrm{k}-4 & 2 \mathrm{k}-9 & 3 \mathrm{k}-16 \\ \mathrm{k}-8 & 2 \mathrm{k}-27 & 3 \mathrm{k}-64\end{array}\right|=0\)

1 1
2 2
3 3
4 4
Shift-I]
Matrix and Determinant

79051 For any \(a, b, c \in R\), the determinant
\(\left|\begin{array}{ccc}\mathbf{b c} & \mathbf{b}+\mathbf{c} & \mathbf{1} \\ \mathbf{c a} & \mathbf{c}+\mathbf{a} & \mathbf{1} \\ \mathbf{a b} & \mathbf{a}+\mathbf{b} & \mathbf{1}\end{array}\right|\) is equal to

1 \(a\left(b^{2}-c^{2}\right)+b\left(c^{2}-a^{2}\right)+c\left(a^{2}-b^{2}\right)\)
2 \(a(b-c)+b(c-a)+c(a-b)\)
3 \((a-b)(b-c)(c-a)\)
4 abc
AP EAMCET-2020-21.09.2020
For More Updates join with Us
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Matrix and Determinant

79047 Let \(A=\left(\begin{array}{cc}x+2 & 3 x \\ 3 & x+2\end{array}\right), B=\left(\begin{array}{cc}x & 0 \\ 5 & x+2\end{array}\right)\). Then all solutions of the equation \(\operatorname{det}(A B)=0\) is

1 \(1,-1,0,2\)
2 \(1,4,0,-2\)
3 \(1,-1,4,3\)
4 \(-1,4,0,3\)
WB JEE-2017
Matrix and Determinant

79048 The linear system of equations
\(\left.\begin{array}{r}
8 x-3 y-5 z=0 \\ 5 x-8 y+3 z=0 \\ 3 x+5 y-8 z=0 \end{array}\right\} \text { has }\)

1 only zero solution
2 only finite number of non-zero solutions
3 no non-zero solution
4 infinitely many non-zero solutions
WB JEE-2017
Matrix and Determinant

79049 The system of equations
\(\lambda x+y+3 z=0\)
\(2 x+\mu y-z=0\)
\(5 x+7 y+z=0\)
has infinitely many solutions in \(\mathrm{R}\). Then,

1 \(y=2, \mu=3\)
2 \(\lambda=1, \mu=2\)
3 \(\lambda=1, \mu=3\)
4 \(\lambda=3, \mu=1\)
WB JEE-2019
Matrix and Determinant

79050 Find the value of ' \(k\) ', if
\(\left|\begin{array}{lll}\mathrm{k}-2 & 2 \mathrm{k}-3 & 3 \mathrm{k}-4 \\ \mathrm{k}-4 & 2 \mathrm{k}-9 & 3 \mathrm{k}-16 \\ \mathrm{k}-8 & 2 \mathrm{k}-27 & 3 \mathrm{k}-64\end{array}\right|=0\)

1 1
2 2
3 3
4 4
Shift-I]
Matrix and Determinant

79051 For any \(a, b, c \in R\), the determinant
\(\left|\begin{array}{ccc}\mathbf{b c} & \mathbf{b}+\mathbf{c} & \mathbf{1} \\ \mathbf{c a} & \mathbf{c}+\mathbf{a} & \mathbf{1} \\ \mathbf{a b} & \mathbf{a}+\mathbf{b} & \mathbf{1}\end{array}\right|\) is equal to

1 \(a\left(b^{2}-c^{2}\right)+b\left(c^{2}-a^{2}\right)+c\left(a^{2}-b^{2}\right)\)
2 \(a(b-c)+b(c-a)+c(a-b)\)
3 \((a-b)(b-c)(c-a)\)
4 abc
AP EAMCET-2020-21.09.2020
NEET DIGITAL LIBRARY
Matrix and Determinant

79047 Let \(A=\left(\begin{array}{cc}x+2 & 3 x \\ 3 & x+2\end{array}\right), B=\left(\begin{array}{cc}x & 0 \\ 5 & x+2\end{array}\right)\). Then all solutions of the equation \(\operatorname{det}(A B)=0\) is

1 \(1,-1,0,2\)
2 \(1,4,0,-2\)
3 \(1,-1,4,3\)
4 \(-1,4,0,3\)
WB JEE-2017
Matrix and Determinant

79048 The linear system of equations
\(\left.\begin{array}{r}
8 x-3 y-5 z=0 \\ 5 x-8 y+3 z=0 \\ 3 x+5 y-8 z=0 \end{array}\right\} \text { has }\)

1 only zero solution
2 only finite number of non-zero solutions
3 no non-zero solution
4 infinitely many non-zero solutions
WB JEE-2017
Matrix and Determinant

79049 The system of equations
\(\lambda x+y+3 z=0\)
\(2 x+\mu y-z=0\)
\(5 x+7 y+z=0\)
has infinitely many solutions in \(\mathrm{R}\). Then,

1 \(y=2, \mu=3\)
2 \(\lambda=1, \mu=2\)
3 \(\lambda=1, \mu=3\)
4 \(\lambda=3, \mu=1\)
WB JEE-2019
Matrix and Determinant

79050 Find the value of ' \(k\) ', if
\(\left|\begin{array}{lll}\mathrm{k}-2 & 2 \mathrm{k}-3 & 3 \mathrm{k}-4 \\ \mathrm{k}-4 & 2 \mathrm{k}-9 & 3 \mathrm{k}-16 \\ \mathrm{k}-8 & 2 \mathrm{k}-27 & 3 \mathrm{k}-64\end{array}\right|=0\)

1 1
2 2
3 3
4 4
Shift-I]
Matrix and Determinant

79051 For any \(a, b, c \in R\), the determinant
\(\left|\begin{array}{ccc}\mathbf{b c} & \mathbf{b}+\mathbf{c} & \mathbf{1} \\ \mathbf{c a} & \mathbf{c}+\mathbf{a} & \mathbf{1} \\ \mathbf{a b} & \mathbf{a}+\mathbf{b} & \mathbf{1}\end{array}\right|\) is equal to

1 \(a\left(b^{2}-c^{2}\right)+b\left(c^{2}-a^{2}\right)+c\left(a^{2}-b^{2}\right)\)
2 \(a(b-c)+b(c-a)+c(a-b)\)
3 \((a-b)(b-c)(c-a)\)
4 abc
AP EAMCET-2020-21.09.2020
Join With Us for More Updates
Matrix and Determinant

79047 Let \(A=\left(\begin{array}{cc}x+2 & 3 x \\ 3 & x+2\end{array}\right), B=\left(\begin{array}{cc}x & 0 \\ 5 & x+2\end{array}\right)\). Then all solutions of the equation \(\operatorname{det}(A B)=0\) is

1 \(1,-1,0,2\)
2 \(1,4,0,-2\)
3 \(1,-1,4,3\)
4 \(-1,4,0,3\)
WB JEE-2017
Matrix and Determinant

79048 The linear system of equations
\(\left.\begin{array}{r}
8 x-3 y-5 z=0 \\ 5 x-8 y+3 z=0 \\ 3 x+5 y-8 z=0 \end{array}\right\} \text { has }\)

1 only zero solution
2 only finite number of non-zero solutions
3 no non-zero solution
4 infinitely many non-zero solutions
WB JEE-2017
Matrix and Determinant

79049 The system of equations
\(\lambda x+y+3 z=0\)
\(2 x+\mu y-z=0\)
\(5 x+7 y+z=0\)
has infinitely many solutions in \(\mathrm{R}\). Then,

1 \(y=2, \mu=3\)
2 \(\lambda=1, \mu=2\)
3 \(\lambda=1, \mu=3\)
4 \(\lambda=3, \mu=1\)
WB JEE-2019
Matrix and Determinant

79050 Find the value of ' \(k\) ', if
\(\left|\begin{array}{lll}\mathrm{k}-2 & 2 \mathrm{k}-3 & 3 \mathrm{k}-4 \\ \mathrm{k}-4 & 2 \mathrm{k}-9 & 3 \mathrm{k}-16 \\ \mathrm{k}-8 & 2 \mathrm{k}-27 & 3 \mathrm{k}-64\end{array}\right|=0\)

1 1
2 2
3 3
4 4
Shift-I]
Matrix and Determinant

79051 For any \(a, b, c \in R\), the determinant
\(\left|\begin{array}{ccc}\mathbf{b c} & \mathbf{b}+\mathbf{c} & \mathbf{1} \\ \mathbf{c a} & \mathbf{c}+\mathbf{a} & \mathbf{1} \\ \mathbf{a b} & \mathbf{a}+\mathbf{b} & \mathbf{1}\end{array}\right|\) is equal to

1 \(a\left(b^{2}-c^{2}\right)+b\left(c^{2}-a^{2}\right)+c\left(a^{2}-b^{2}\right)\)
2 \(a(b-c)+b(c-a)+c(a-b)\)
3 \((a-b)(b-c)(c-a)\)
4 abc
AP EAMCET-2020-21.09.2020