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Let matrix $A = [\begin{matrix} 5 & - 3 & 0 \\ - 3 & 5 & 0 \\ 0 & 0 & 2 \end{matrix}]$ , $X$ be a non-zero matrix of order $3 \times 1$ and $c$ be a real number. If $A^{2} X = c A X$ . Then the number of distinct values of $c$ is

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Important Questions on Matrices and Determinants

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

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

HARD

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

Let

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

. If

A^{2} + γ A + 18 I = O

, then

det (A)

is equal to _______.

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

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 :

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

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

HARD

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

If A =

[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & - 2 & 4 \end{matrix}]

, 6A^-1 = A²+ cA + dI, then (c, d) is

EASY

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

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

and

A^{2} = I

, then

A^{- 1}

is equal to

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

A^{3} = 0

, then

I + A + A^{2}

equals

HARD

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

Consider matrix

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

A^{- 1} = α I + β A

where

α, β \in R,

then

α + β

is equal to (Where

A^{- 1}

denotes inverse of matrix

A

) -

HARD

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

A^{3} = O

, then

I + A + A^{2}

equals

EASY

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

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

and

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

, then the correct option is

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

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

is a root of polynomial

x^{3} - 6 x^{2} + 7 x + k = 0,

then the value of

k

EASY

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

A

is solution of

x^{2} - 3 x - 7 = 0

and

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

, then

A^{- 1}

equals

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

The characteristic roots of the matrix

[\begin{matrix} 1 0 0 \\ 2 3 0 \\ 4 5 6 \end{matrix}]

are

EASY

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

A square, non-singular matrix

A

satisfies

A^{2} - A + 2 I = 0

, then

A^{- 1}

is equal to

EASY

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

A^{2} - A + I = O,

then the inverse of A is

EASY

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

A

3 \times 3

square matrix whose characteristic polynomial equations is

λ^{3} - 3 λ^{2} + 4 = 0,

then trace of

adj A

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

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

then

A^{- 1}

equals

HARD

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

The characteristic roots of the matrix

A = |\begin{matrix} a & 0 & 0 \\ x & b & 0 \\ y & z & c \end{matrix}|

are

EASY

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

A square, non-singular matrix

A

satisfies

A^{2} - A + 2 I = 0

, then

A^{- 1}

is equal to

EASY

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

A

is a non-singular matrix and

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

then

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

Let matrix A=5-30-350002, X be a non-zero matrix of order 3×1 and c be a real number. If A2X=cAX. Then the number of distinct values of c is

Important Questions on Matrices and Determinants

Learn and Prepare for any exam you want !

Let matrix $A = [\begin{matrix} 5 & - 3 & 0 \\ - 3 & 5 & 0 \\ 0 & 0 & 2 \end{matrix}]$ , $X$ be a non-zero matrix of order $3 \times 1$ and $c$ be a real number. If $A^{2} X = c A X$ . Then the number of distinct values of $c$ is