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

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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 -

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Important Questions on Matrices and Determinants

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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

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 9

If

a_{1}, a_{2}, .... a_{n}, a_{n + 1} .....

are in

GP

and

a_{i} > 0 \forall i

, then

|\begin{matrix} {loga}_{n} & {loga}_{n + 2} & {loga}_{n + 4} \\ {loga}_{n + 6} & {loga}_{n + 8} & {loga}_{n + 10} \\ {loga}_{n + 12} & {loga}_{n + 14} & {loga}_{n + 16} \end{matrix}|

is equal to -

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

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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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 11

For positive numbers

x, y

and

z

, the numerical value of the determinant

|\begin{matrix} 1 & \log_{x} y & \log_{x} z \\ \log_{y} x & 1 & \log_{y} z \\ \log_{z} x & \log_{z} y & 1 \end{matrix}|

is _____

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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}]