Let A , be a 3 × 3 matrix, such that A 2 - 5 A + 7 I = O . Statement - I : A - 1 = 1 7 5 I - A . Statement - II : The polynomial A 3 - 2 A 2 - 3 A + I ,can be reduced to 5 A - 4 I . Then :

Statement - I is true, but Statement - II is false

Statement - I is false, but Statement - II is true

The inverse of the matrix 1 0 0 3 3 0 5 2 - 1 is

- 1 3 - 3 0 0 3 - 1 0 - 9 - 2 3

- 1 3 3 0 0 3 - 1 0 - 9 - 2 - 3

- 1 3 - 3 0 0 - 3 - 1 0 - 9 - 2 3

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The characteristic roots of the matrix $[\begin{matrix} 1 0 0 \\ 2 3 0 \\ 4 5 6 \end{matrix}]$ are

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Important Questions on Matrices and Determinants

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Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

Let

A

be a

2 \times 2

matrix with real entries such that zero is the only solution of the equation

det (A - x I) = 0

. Then

EASY

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

A = [\begin{matrix} 2 x & 0 \\ x & x \end{matrix}]

and

A^{- 1} = [\begin{matrix} 1 & 0 \\ - 1 & 2 \end{matrix}]

,

then

x =

HARD

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

Let

A

, be a

3 \times 3

matrix, such that

A^{2} - 5 A + 7 I = O .

Statement - I :

A^{- 1} = \frac{1}{7} (5 I - A) .

Statement - II : The polynomial

A^{3} - 2 A^{2} - 3 A + I

,can be reduced to

5 (A - 4 I) .

Then :

EASY

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

A = [\begin{matrix} 2 & 2 \\ 9 & 4 \end{matrix}]

and

I = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}],

then

10 A^{- 1}

, is equal to.

EASY

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

Inverse of a diagonal non-singular matrix is

EASY

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

A

is a non-singular matrix and

(A + I) (A - I) = 0

then

A + A^{- 1} = \dots \dots

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

Let

A

be any

3 \times 3

invertible matrix. Then which one of the following is not always true?

EASY

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

(\begin{array}{l} 2 & 1 \\ 3 & 2 \end{array}) A = (\begin{array}{l} 1 & 0 \\ 0 & 1 \end{array})

, then the matrix

A

EASY

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

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

and

B = [\begin{matrix} 3 \\ 1 \end{matrix}], A X = B

, then

X

is equal to

HARD

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

The inverse of the matrix

[\begin{matrix} 1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & - 1 \end{matrix}]

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

Let

M = [\begin{matrix} \sin^{4} θ & - 1 - \sin^{2} θ \\ 1 + \cos^{2} θ & \cos^{4} θ \end{matrix}] = α I + β M^{- 1},

where

α = α (θ)

and

β = β (θ)

are real number, and

I

is the

2 \times 2

identity matrix. If

α^{*}

is the minimum of the set {

α (θ) : θ \in [0, 2 π)}

and

β^{*}

is the minimum of the set

\{β (θ) : θ \in [0, 2 π)\},

then the value of

α^{*} + β^{*}

HARD

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

Let

A = (\begin{matrix} 4 & - 2 \\ α & β \end{matrix})

. If

A^{2} + γ A + 18 I = O

, then

det (A)

is equal to _______.

EASY

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

The inverse of matrix is

[\begin{matrix} 2 & 5 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & 3 \end{matrix}]

EASY

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

B = [\begin{matrix} 5 & 2 α & 1 \\ 0 & 2 & 1 \\ α & 3 & - 1 \end{matrix}]

is the inverse of a

3 \times 3

matix

A,

then the sum of all values of

α

for which

d e t (A) + 1 = 0,

is:

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Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

A^{- 1} = \frac{1}{11} [\begin{matrix} - 3 & 4 \\ 5 & - 3 \end{matrix}]

, then

A =

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Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

Which of the following matrix is invertible? $A_{1} = [\begin{array}{r} 4 & 2 \\ 2 & 1 \end{array}]$ , $A_{2} = [\begin{matrix} - 1 & - 2 & 3 \\ 4 & 5 & 7 \\ 2 & 4 & - 6 \end{matrix}]$ , $A_{3} = [\begin{matrix} 1 & 0 & 0 \\ 5 & 2 & 1 \\ 7 & 2 & 1 \end{matrix}]$ , $A_{4} = [\begin{array}{l} 1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1 \end{array}]$ .

EASY

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

A = [\begin{array}{r} 3 & - 3 & 4 \\ 2 & - 3 & 4 \\ 0 & - 1 & 1 \end{array}]

then

{(A^{2})}^{- 1} =

EASY

Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

A = [\begin{matrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{matrix}]

,

then the sum of all the diagonal entries of

A^{- 1}

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Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

A = [\begin{matrix} 1 & 5 \\ λ & 10 \end{matrix}], A^{- 1} = α A + β I

and

α + β = - 2

, then

4 α^{2} + β^{2} + λ^{2}

is equal to :

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Mathematics>Algebra>Matrices and Determinants>Inverse of a Matrix

Let

A = (\begin{matrix} 1 & 2 \\ - 2 & - 5 \end{matrix})

. Let

α, β \in ℝ

be such that

α A^{2} + β A = 2 I

. Then

α + β

is equal to

The characteristic roots of the matrix1 0 02 3 04 5 6 are

Important Questions on Matrices and Determinants

Learn and Prepare for any exam you want !

The characteristic roots of the matrix $[\begin{matrix} 1 0 0 \\ 2 3 0 \\ 4 5 6 \end{matrix}]$ are