Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 44

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IMPORTANT

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If $n^{th}$ order square matrix $A$ is an orthogonal, then $|adj (adj A)|$ is

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Important Questions on Matrices

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 45

Let

a

and

b

be two real numbers such that

a > 1, b > 1

. If

A = (\begin{matrix} a & 0 \\ 0 & b \end{matrix})

, then

\lim_{n \to \infty} {(A^{n})}^{- 1}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 46

If

A = {[a_{i j}]}_{4 \times 4},

such that

a_{i j} = \{\begin{cases} 2, & when i = j \\ 0, & when i \neq j \end{cases}

, then

\{\frac{det (adj (adj A))}{7}\}

is (where

\{.\}

represents fractional part function)

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 47

If

A

is an involuntary matrix given by

A = [\begin{array}{l} 0 & 1 & - 1 \\ 4 & - 3 & 4 \\ 3 & - 3 & 4 \end{array}]

then the inverse of

\frac{A}{2}

will be

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 48

If

A

is a nonsingular matrix such that

A A^{T} = A^{T} A

and

B = A^{- 1} A^{T}

, then matrix

B

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 49

If

P

is an orthogonal matrix and

Q = P A P^{T}

and

x = P^{T} Q^{1000} P

, then

x^{- 1}

is, where

A

is involutaoy matrix

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 50

If

A

and

B

are two nonsingular matrices of the same order such that

B^{r} = I

, for some positive integer

r > I

, then

A^{- 1} B^{r - 1} A - A^{- 1} B^{- 1} A =

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 51

If

adj B = A, |P| = |Q| = 1

, then

adj (Q^{- 1} B P^{- 1})

is,

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 52

If

A

is non-singular and

(A - 2 I) (A - 4 I) = O

, then

\frac{1}{6} A + \frac{4}{3} A^{- 1}

is equal to