Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-4>Q 42

HARD

JEE Main/Advance

IMPORTANT

Earn 100

If $A$ is an orthogonal matrix and $B = A P$ where $P$ is a non singular matrix then show that the matrix $P B^{- 1}$ is also orthogonal.

Important Questions on Matrices and Determinants

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 1

The value of determinant

= {(A^{T} A)}^{- 1} {(P^{T})}^{- 1} P^{T}

is equal to -

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 2

If

| \begin{matrix} \sin 2 x & \cos^{2} x & \cos 4 x \\ \cos^{2} x & \cos 2 x & \sin^{2} x \\ \cos^{4} x & \sin^{2} x & \sin 2 x \end{matrix} | = a_{0} + a_{1} (s i n x) + a_{2} (\sin^{2} x) + ... + a_{0} (\sin^{n} x)

then the value of

a_{0}

is -

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 3

The value of the determinant

|\begin{matrix} - a & b & c \\ a & - b & c \\ a & b & - c \end{matrix}|

is equal to -

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 4

For any

Δ A B C

, the value of determinant

| \begin{matrix} \sin^{2} A & c o t A & 1 \\ \sin^{2} B & c o t B & 1 \\ \sin^{2} C & c o t C & 1 \end{matrix} |

is equal to-

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 5

If

D_{p} = | \begin{matrix} p & 15 & 8 \\ p^{2} & 35 & 9 \\ p^{3} & 25 & 10 \end{matrix} |

,then

D_{1} + D_{2} + D_{3} + D_{4} + D_{5}

is equal to -

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 6

If

A + B + C = π

then

| \begin{matrix} \sin (A + B + C) & s i n B & c o s C \\ - s i n B & 0 & t a n A \\ \cos (A + B) & - t a n A & 0 \end{matrix} |

is equal to-

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 7

The number of real values of

x

satisfying

| \begin{matrix} x & 3 x + 2 & 2 x - 1 \\ 2 x - 1 & 4 x & 3 x + 1 \\ 7 x - 2 & 17 x - 6 & 12 x - 1 \end{matrix} | = 0

is -

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 8

If

a, b, c

are

p t h

,

q t h

and

r t h

terms of a GP, then

|\begin{array}{l} \log a & p & 1 \\ \log b & q & 1 \\ \log c & r & 1 \end{array}|

is equal to