Matrices and Determinants Questions

MathematicsMatrices and Determinants115 Questions Found

MathematicsProperties of DeterminantsJEE Main 2014Moderate

If $α, β \neq = 0$ , and $f (n) = α^{n} + β^{n}$ and $3 1 + f (1) 1 + f (2) 1 + f (1) 1 + f (2) 1 + f (3) 1 + f (2) 1 + f (3) 1 + f (4) = K (1 - α)^{2} (1 - β)^{2} (α - β)^{2}$ , then $K$ is equal to:

(A)

1

(B)

- 1

(C)

α β

(D)

\frac{1}{α β}

Answer:A

MathematicsAlgebraic Operations on MatricesJEE Main 2015Easy

View in:English Hindi

If $A = 12 a 212 2 - 2 b$ is a matrix satisfying the equation $A A^{T} = 9 I$ , where $I$ is $3 \times 3$ identity matrix, then the ordered pair $(a, b)$ is equal to:

(A)

(2, 1)

(B)

(- 2, - 1)

(C)

(2, - 1)

(D)

(- 2, 1)

Answer:B

MathematicsSolution of System of Linear Equations (Matrix Method and Cramer's Rule)JEE Main 2015Easy

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The set of all values of $λ$ for which the system of linear equations: $2 x_{1} - 2 x_{2} + x_{3} = λ x_{1}$ , $2 x_{1} - 3 x_{2} + 2 x_{3} = λ x_{2}$ , $- x_{1} + 2 x_{2} = λ x_{3}$ has a non-trivial solution

(A)

contains two elements

(B)

contains more than two elements

(C)

is an empty set

(D)

is a singleton

Answer:A

MathematicsAdjoint and Inverse of a MatrixJEE Main 2016Easy

View in:English Hindi

If $A = [5 a 3 - b 2]$ and $A adj A = A A^{T}$ , then $5 a + b$ is equal to:

(A)

4

(B)

13

(C)

- 1

(D)

5

Answer:D

MathematicsSolution of System of Linear Equations (Matrix Method and Cramer's Rule)JEE Main 2016Moderate

View in:English Hindi

The system of linear equations $x + λ y - z = 0$ , $λ x - y - z = 0$ , $x + y - λ z = 0$ has a non-trivial solution for:

(A)

exactly two values of

λ

(B)

exactly three values of

λ

(C)

infinitely many values of

λ

(D)

exactly one value of

λ

Answer:B

...11

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If α,β=0, and f(n)=αn+βn and ​31+f(1)1+f(2)​1+f(1)1+f(2)1+f(3)​1+f(2)1+f(3)1+f(4)​​=K(1−α)2(1−β)2(α−β)2, then K is equal to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If A=​12a​212​2−2b​​ is a matrix satisfying the equation AAT=9I, where I is 3×3 identity matrix, then the ordered pair (a,b) is equal to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If A=[5a3​−b2​] and A adj A=AAT, then 5a+b is equal to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The system of linear equations x+λy−z=0, λx−y−z=0, x+y−λz=0 has a non-trivial solution for:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If α,β=0, and f(n)=αn+βn and ​31+f(1)1+f(2)​1+f(1)1+f(2)1+f(3)​1+f(2)1+f(3)1+f(4)​​=K(1−α)2(1−β)2(α−β)2, then K is equal to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If A=​12a​212​2−2b​​ is a matrix satisfying the equation AAT=9I, where I is 3×3 identity matrix, then the ordered pair (a,b) is equal to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If A=[5a3​−b2​] and A adj A=AAT, then 5a+b is equal to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The system of linear equations x+λy−z=0, λx−y−z=0, x+y−λz=0 has a non-trivial solution for:

If $α, β \neq = 0$ , and $f (n) = α^{n} + β^{n}$ and $3 1 + f (1) 1 + f (2) 1 + f (1) 1 + f (2) 1 + f (3) 1 + f (2) 1 + f (3) 1 + f (4) = K (1 - α)^{2} (1 - β)^{2} (α - β)^{2}$ , then $K$ is equal to:

If $A = 12 a 212 2 - 2 b$ is a matrix satisfying the equation $A A^{T} = 9 I$ , where $I$ is $3 \times 3$ identity matrix, then the ordered pair $(a, b)$ is equal to:

If $A = [5 a 3 - b 2]$ and $A adj A = A A^{T}$ , then $5 a + b$ is equal to:

The system of linear equations $x + λ y - z = 0$ , $λ x - y - z = 0$ , $x + y - λ z = 0$ has a non-trivial solution for:

If $α, β \neq = 0$ , and $f (n) = α^{n} + β^{n}$ and $3 1 + f (1) 1 + f (2) 1 + f (1) 1 + f (2) 1 + f (3) 1 + f (2) 1 + f (3) 1 + f (4) = K (1 - α)^{2} (1 - β)^{2} (α - β)^{2}$ , then $K$ is equal to:

If $A = 12 a 212 2 - 2 b$ is a matrix satisfying the equation $A A^{T} = 9 I$ , where $I$ is $3 \times 3$ identity matrix, then the ordered pair $(a, b)$ is equal to:

If $A = [5 a 3 - b 2]$ and $A adj A = A A^{T}$ , then $5 a + b$ is equal to:

The system of linear equations $x + λ y - z = 0$ , $λ x - y - z = 0$ , $x + y - λ z = 0$ has a non-trivial solution for: