EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 10th April 2016>Q 140

HARD

JEE Main

IMPORTANT

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Let $A$ , be a $3 \times 3$ matrix, such that $A^{2} - 5 A + 7 I = O .$
Statement - I : $A^{- 1} = \frac{1}{7} (5 I - A) .$
Statement - II : The polynomial $A^{3} - 2 A^{2} - 3 A + I$ ,can be reduced to $5 (A - 4 I) .$ Then :

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Important Questions on Matrices and Determinants

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 10th April 2016>Q 141

If

A = [\begin{matrix} - 4 & - 1 \\ 3 & 1 \end{matrix}]

, then the determinant of the matrix

(A^{2016} - 2 A^{2015} - A^{2014})

is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 10th April 2015>Q 142

The least value of the product

x y z

(such that

x, y and z

are positive real numbers) for which the determinant

|\begin{matrix} x \\ 1 \\ 1 \end{matrix} \begin{matrix} 1 \\ y \\ 1 \end{matrix} \begin{matrix} 1 \\ 1 \\ z \end{matrix}|

is non-negative is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 10th April 2015>Q 143

If

A = [\begin{matrix} 0 \\ 1 \end{matrix} \begin{matrix} - 1 \\ 0 \end{matrix}]

, then which one of the following statements is not correct?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 4th April 2015>Q 144

If $A = [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ a & 2 & b \end{matrix}]$ 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

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 4th April 2015>Q 145

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,

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 11th April 2015>Q 146

If

A

is a

3 \times 3

matrix such that

|5 a d j A| = 5

, then

|A|

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 11th April 2015>Q 147

If

|\begin{matrix} x^{2} + x & x + 1 & x - 2 \\ 2 x^{2} + 3 x - 1 & 3 x & 3 x - 3 \\ x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{matrix}| = a x - 12

, then

a

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 19th April 2014>Q 148

If

Δ_{r} = |\begin{matrix} r & 2 r - 1 & 3 r - 2 \\ \frac{n}{2} & n - 1 & a \\ \frac{1}{2} n (n - 1) & {(n - 1)}^{2} & \frac{1}{2} (n - 1) (3 n + 4) \end{matrix}|

, then the value of

\sum_{r = 1}^{n - 1} Δ_{r}