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

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IMPORTANT

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If $p x^{4} + q x^{3} + r x^{3} + s x + t = | \begin{matrix} x^{2} + 3 x & x - 1 & x + 3 \\ x + 1 & 2 - x & x - 3 \\ x - 3 & x + 4 & 3 x \end{matrix} |$ then $t$ is equal to -

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Important Questions on Matrices and Determinants

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 12

If

a, b & c > 0

and

x, y, x \in R

, then the determinant

| \begin{matrix} {(a^{x} + a^{- x})}^{2} & {(a^{x} - a^{- x})}^{2} & 1 \\ {(b^{y} + b^{- y})}^{2} & {(b^{y} - b^{- y})}^{2} & 1 \\ {(c^{z} + c^{- z})}^{2} & (c^{z} - c^{- z}) & 1 \end{matrix} |

is equal to :

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 13

For a non-zero real

a, b

and

c

| \begin{matrix} \frac{a^{2} + b^{2}}{c} & c & c \\ a & \frac{b^{2} + c^{2}}{a} & a \\ b & b & \frac{c^{2} + a^{2}}{b} \end{matrix} | = α

a b c

, then the values of

α

is ?

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 14

Find the number of solution(s) for the equation

| \begin{matrix} {(1 + x)}^{2} & {(1 - x)}^{2} & - (2 + x^{2}) \\ 2 x + 1 & 3 x & 1 - 5 x \\ x + 1 & 2 x & 2 - 3 x \end{matrix} | + | \begin{matrix} {(1 + x)}^{2} & 2 x + 1 & x + 1 \\ {(1 - x)}^{2} & 3 x & 2 x \\ 1 - 2 x & 3 x - 2 & 2 x - 3 \end{matrix} | = 0

.

HARD

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 15

Let a determinant is given by

A = [\begin{matrix} \begin{array}{l} a & b & c \\ p & q & r \\ x & y & z \end{array} \end{matrix}]

and suppose determinant

A = 6

. If

B = [\begin{matrix} \begin{matrix} p + x & q + y & r + z \\ a + x & b + y & c + z \\ a + p & b + q & c + r \end{matrix} \end{matrix}]

EASY

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 16

If

a \neq b \neq c

and

| \begin{matrix} a & b & c \\ a^{2} & b^{2} & c^{2} \\ b + c & c + a & a + b \end{matrix} | = 0

then -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 17

If

a, b

&

c

are nonzero real number, then

| \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 equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 18

If

f (x) = |\begin{matrix} 1 & x & x + 1 \\ 2 x & x (x - 1) & (x + 1) x \\ 3 x (x - 1) & x (x - 1) (x - 2) & (x + 1) x (x - 1) \end{matrix}|

, then

f (100)

is equal to

EASY

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 19

The value of the determinant

| \begin{matrix} a & b & 0 \\ 0 & a & b \\ b & 0 & a \end{matrix} |

is equal to -