Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Miscellaneous Exercise 2(B)>Q 6

EASY

12th Maharashtra Board

IMPORTANT

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If $A = [\begin{matrix} λ & 1 \\ - 1 & - λ \end{matrix}]$ then $A^{- 1}$ does not exist if $λ =$

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Important Questions on Matrices

HARD

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Miscellaneous Exercise 2(B)>Q 7

If

A = [\begin{matrix} \cos α & - \sin α \\ \sin α & \cos α \end{matrix}]

then

A^{- 1} =

HARD

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Miscellaneous Exercise 2(B)>Q 8

If

F (α) = [\begin{matrix} \cos α & - \sin α & 0 \\ \sin α & \cos α & 0 \\ 0 & 0 & 1 \end{matrix}]

where

α \in R

then

{[F (α)]}^{- 1}

is

=

HARD

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Miscellaneous Exercise 2(B)>Q 9

The inverse of

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

is

MEDIUM

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Miscellaneous Exercise 2(B)>Q 10

The inverse of a symmetric matrix is -

MEDIUM

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Miscellaneous Exercise 2(B)>Q 11

For a

2 \times 2

matrix

A

, if

A (adj A) = [\begin{matrix} 10 & 0 \\ 0 & 10 \end{matrix}]

then determinant A equals

EASY

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Miscellaneous Exercise 2(B)>Q 12

If

A^{'} = - \frac{1}{2} [\begin{matrix} 1 & - 4 \\ - 1 & 2 \end{matrix}]

then

A =

HARD

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Miscellaneous Exercise 2(B)>Q 1)

Solve the following equations by the methods of inversion

2 x - y = - 2, x + 5 y = 5

HARD

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Miscellaneous Exercise 2(B)>Q 1)

Solve the following equations by the method of inversion

$x + y + z = 1, 2 x + 3 y + 2 z = 2$ and $a x + a y + 2 a z = 4$