Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 58

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The absolute value of the determinant $|\begin{matrix} - 1 & 2 & 1 \\ 3 + 2 \sqrt{2} & 2 + 2 \sqrt{2} & 1 \\ 3 - 2 \sqrt{2} & 2 - 2 \sqrt{2} & 1 \end{matrix}|$ is:

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Important Questions on Matrices and Determinants

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 59

If

α, β & γ

are the roots of the equation

x^{3} + p x + q = 0,

then the value of the determinant

|\begin{array}{l} α & β & γ \\ β & γ & α \\ γ & α & β \end{array}| =

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 60

If

a, b, c > 0

&

x, y, z \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})}^{2} & 1 \end{matrix}| =

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 61

If

a, b

&

c

are non-zero real numbers, then

D = |\begin{array}{l} 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{array}| =

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 62

The determinant

|\begin{array}{l} b_{1} + c_{1} & c_{1} + a_{1} & a_{1} + b_{1} \\ b_{2} + c_{2} & c_{2} + a_{2} & a_{2} + b_{2} \\ b_{3} + c_{3} & c_{3} + a_{3} & a_{3} + b_{3} \end{array}| =

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 63

If

x, y, z \in R & Δ = |\begin{matrix} x & x + y & x + y + z \\ 2 x & 5 x + 2 y & 7 x + 5 y + 2 z \\ 3 x & 7 x + 3 y & 9 x + 7 y + 3 z \end{matrix}| = - 16,

then value of

x

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 64

The determinant

|\begin{matrix} \cos (θ + ϕ) & - \sin (θ + ϕ) & \cos 2 ϕ \\ sinθ & cosθ & sinϕ \\ - cosθ & sinθ & cosϕ \end{matrix}|

is:

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 65

Let $A$ be set of all determinants of order $3$ with entries $0$ or $1, B$ be the subset of $A$ consisting of all determinants with value $1$ and $C$ be the subset of $A$ consisting of all determinants with value $- 1 .$ Then

STATEMENT -1: The number of elements in set $B$ is equal to number of elements in set $C .$ and

STATEMENT -2: $(B \cap C) \subset A$

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 66

If

A = [\begin{array}{l} 1 & 2 \\ 2 & 1 \end{array}],

then

adj A =