RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 172

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IMPORTANT

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If $a, b, c$ are non zero real numbers then the value of $|\begin{matrix} b^{2} c^{2} & b c & b + c \\ c^{2} a^{2} & c a & c + a \\ a^{2} b^{2} & a b & a + b \end{matrix}|$ is

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Important Questions on Matrices and Determinants

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IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 173

The sum of the products of the elements of any row of a determinant

A

with the corresponding cofactors of the same row is always equal to

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IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 174

If

A

and

B

are square matrices and

A^{- 1}

and

B^{- 1}

exist then

{(A B)}^{- 1} =

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IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 175

The value of

|\begin{matrix} 41 & 42 & 43 \\ 44 & 45 & 46 \\ 47 & 48 & 49 \end{matrix}| =

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IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 176

If

A = [\begin{matrix} 2 & 3 \\ 4 & 6 \end{matrix}]

then

A^{- 1} =

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IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 177

If

5

is one root of the equation

|\begin{matrix} x & 3 & 7 \\ 2 & x & - 2 \\ 7 & 8 & x \end{matrix}| = 0

then the other two roots of the equation are

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IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 178

For a real number

\propto

, let

A (\propto)

denote the matrix, then for real numbers

\propto_{1}

and

\propto_{2}

,

A (\propto_{1}) A (\propto_{2})

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IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 179

For how many values of

x

in the closed interval

[- 4, - 1]

, the matrix

[\begin{matrix} 3 & - 1 + x & 2 \\ 3 & - 1 & x + 2 \\ x + 3 & - 1 & 2 \end{matrix}]

is singular.

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IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 180

Inverse of the matrix

|\begin{matrix} 1 & - 2 \\ 3 & 4 \end{matrix}|

is