Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 10

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If $[\begin{matrix} α & β \\ γ & - α \end{matrix}]$ is to be the square root of two-rowed unit matrix, then $α, β$ and $γ$ should satisfy the relation

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Important Questions on Matrices

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 11

If

A = [\begin{matrix} i & - i \\ - i & i \end{matrix}]

and

B = [\begin{array}{rr} 1 & - 1 \\ - 1 & 1 \end{array}]

, then

A^{8}

equals

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 12

If $[\begin{matrix} 2 & - 1 \\ 1 & 0 \\ - 3 & 4 \end{matrix}] A = [\begin{matrix} - 1 & - 8 & - 10 \\ 1 & - 2 & - 5 \\ 9 & 22 & 15 \end{matrix}]$ , then sum of all the elements of matrix $A$ is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 13

For each real

x

,

- 1 < x < 1

. Let

A (x)

be the matrix

{(1 - x)}^{- 1} [\begin{matrix} 1 & - x \\ - x & 1 \end{matrix}]

and

z = \frac{x + y}{1 + x y}

, Then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 14

If

A = [\begin{matrix} 0 & \tan α / 2 \\ - \tan α / 2 & 0 \end{matrix}]

and

I

is a

2 \times 2

unit matrix, then

(I - A) [\begin{matrix} \cos α & - \sin α \\ \sin α & \sin α \end{matrix}]

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 15

The number of solutions of the matrix equation

X^{2} = [\begin{matrix} 1 & 1 \\ 2 & 3 \end{matrix}]

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 16

If

A = [\begin{matrix} a & b \\ c & d \end{matrix}]

(where

b c \neq 0

) satisfies the equations

x^{2} + k = 0,

then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 17

Consider three matrices

A = [\begin{matrix} 2 & 1 \\ 4 & 1 \end{matrix}], B = [\begin{matrix} 3 & 4 \\ 2 & 3 \end{matrix}]

, and

C = [\begin{matrix} 3 & - 4 \\ - 2 & 3 \end{matrix}]

. Then the value of the sum

t r (A) + t r (\frac{A B C}{2}) + t r (\frac{A {(B C)}^{2}}{4}) + t r (\frac{A {(B C)}^{3}}{8}) + . . . . . . \infty

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 18

If

{[\begin{matrix} \cos \frac{2 π}{7} & - \sin \frac{2 π}{7} \\ \sin \frac{2 π}{7} & \cos \frac{2 π}{7} \end{matrix}]}^{k} = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

then the least positive integral value of $k$ is