Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 4 - Matrices & Determinants>Exercise 1>Q 33

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If $I_{n}$ is the identity matrix of order $n$ , then rank of $I_{n}$ is

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Important Questions on Matrices & Determinants

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 4 - Matrices & Determinants>Exercise 1>Q 34

If the points

(x_{1}, y_{1})

,

(x_{2}, y_{2})

and

(x_{3}, y_{3})

are collinear, then the rank of the matrix

[\begin{array}{l} x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1 \end{array}]

will always be less, than

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 4 - Matrices & Determinants>Exercise 1>Q 35

If

A = [\begin{array}{l} 2 & 0 & 0 \\ 2 & 2 & 0 \\ 2 & 2 & 2 \end{array}]

, then

adj (adj A)

is equal to

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 4 - Matrices & Determinants>Exercise 1>Q 36

If

A = [\begin{array}{l} 3 & 4 \\ 5 & 7 \end{array}],

then

A \cdot (adj A)

is equal to

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 4 - Matrices & Determinants>Exercise 1>Q 37

If

A = [\begin{matrix} p & q \\ - q & p \end{matrix}], B = [\begin{matrix} r & s \\ - s & r \end{matrix}]

, then

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 4 - Matrices & Determinants>Exercise 1>Q 38

If

∆ (x) = |\begin{matrix} 1 & \cos x & 1 - \cos x \\ 1 + \sin x & \cos x & 1 + \sin x - \cos x \\ \sin x & \sin x & 1 \end{matrix}|

, then

\int_{0}^{π / 4} ∆ (x) d x

is equal to

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 4 - Matrices & Determinants>Exercise 1>Q 39

If

[\begin{matrix} 1 & 0 \\ 3 & - 4 \end{matrix}] + [\begin{matrix} a & 1 \\ - 1 & b \end{matrix}] = [\begin{matrix} 2 & 1 \\ 2 & - 2 \end{matrix}],

then value of

a, b

are

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 4 - Matrices & Determinants>Exercise 1>Q 40

The digits

A, B

and

C

are such that the three digit numbers

A 88, 6 B 8, 86 C

are divisible by

72

, then the determinant

|\begin{array}{l} A & 6 & 8 \\ 8 & B & 6 \\ 8 & 8 & C \end{array}|

is divisible by

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 4 - Matrices & Determinants>Exercise 2>Q 1

If

k [\begin{matrix} - 1 & 2 & 2 \\ 2 & - 1 & 2 \\ 2 & 2 & - 1 \end{matrix}]

is an orthogonal matrix, then

k

is equal to