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

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IMPORTANT

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

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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 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

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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 -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 20

An equilateral triangle has each of its sides of length

6 cm

. If

(x_{1}, y_{1}); (x_{2}, y_{2})

&

(x_{3}, y_{3})

are its vertices then the value of the determinant,

{|\begin{matrix} x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1 \end{matrix}|}^{2}

is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 21

If the system of equations

x + 2 y + 3 z = 4, x + p y + 2 z = 3, x + 4 y + μ z = 3

has an infinite number of solutions, then -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 22

If

A - 2 B = [\begin{matrix} 1 & 5 \\ 3 & 7 \end{matrix}] a n d 2 A - 3 B = [\begin{matrix} - 2 & 5 \\ 0 & 7 \end{matrix}]

then matrix

B

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 23

If

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

, then

A_{α} A_{β}

is equal to -