Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 28

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Let $a_{i j}$ denote the element of the $i^{t h}$ row and $j^{t h}$ column in a $3 \times 3$ matrix and let $a_{i j} = - a_{j j}$ for every $i$ and $j$ then this matrix is an -

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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-2>Q 29

Let

A

be an invertible matrix then which of the following is/are true :

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 30

If

A = [\begin{matrix} 1 & 9 & - 7 \\ i & ω^{n} & 8 \\ 1 & 6 & ω^{2 n} \end{matrix}]

and

i = \sqrt{- 1}

is complex cube root of unity, then

t r (A)

will be-

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 31

If

A = [\begin{array}{l} a & b \\ c & d \end{array}]

satisfies the equation

x^{2} + k = 0

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 32

If

A

and

B

are invertible matrices, which one of the following statement is/are correct -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 33

Matrix

[\begin{matrix} a & b & (a α - b) \\ b & c & (b α - c) \\ 2 & 1 & 0 \end{matrix}]

is non invertible if

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 34

Let

A^{- 1} = [\begin{matrix} 1 & - 1 & 2 \\ - 1 & 2 & 1 \\ 2 & 1 & - 1 \end{matrix}]

, then -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 35

Let

A = [\begin{matrix} 0 & \tan θ & 2 \\ - \tan θ & 0 & \sec θ \\ - 2 & - \sec θ & 0 \end{matrix}]

, where

θ \neq (2 n + 1) \frac{π}{2}

&

B = \sum_{r = 1}^{5} A^{(2 r - 1)}

then which of following statement is correct

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 36

If the lines

a x + y + 1 = 0, x + b y + 1 = 0

&

x + y + c = 0

where

a, b

&

c

are distinct real numbers different from

1

are concurrent, then the value of

\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} =