Mathematics · JEE

Online Practice: Matrices, algebra of matrices, type of matrices for JEE

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Q1MathsUnit 3: Matrices and Determinants

\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]

is an example of

Q2MathsUnit 3: Matrices and Determinants

For any square matrix

\boldsymbol{A}, \boldsymbol{A}+\boldsymbol{A}^{T}

Q3MathsUnit 3: Matrices and Determinants

Assertion

\mathbf{f}[\boldsymbol{x} \mathbf{1}]\left[\begin{array}{cc}\mathbf{1} & \mathbf{0} \\ -\mathbf{2} & \mathbf{3}\end{array}\right]\left[\begin{array}{c}\boldsymbol{x} \\ -\mathbf{5}\end{array}\right]=\mathbf{0},

then value of

x

is either- 3 or 5 Reason Two matrices

\left[\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y} \\ \boldsymbol{u} & \boldsymbol{v}\end{array}\right]

\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right]

are equal if

\&

only if their corresponding entries are equal \& only if their corresponding entries are equal

Q4MathsUnit 3: Matrices and Determinants

The matrix

\boldsymbol{B}

Q5MathsUnit 3: Matrices and Determinants

Suppose

A

is any

3 \times 3

non-singular matrix and

(\boldsymbol{A}-\mathbf{3} \boldsymbol{I})(\boldsymbol{A}-\mathbf{5} \boldsymbol{I})=\boldsymbol{O}

where

\boldsymbol{I}=\boldsymbol{I}_{3}

and

\boldsymbol{O}=\boldsymbol{O}_{3},

\boldsymbol{\alpha} \boldsymbol{A}+

\beta A^{-1}=4 I,

then

\alpha+\beta

is equal to

Q6MathsUnit 3: Matrices and Determinants

\boldsymbol{A}=\left[\begin{array}{cc}-\boldsymbol{i} & \mathbf{0} \\ \mathbf{0} & \boldsymbol{i}\end{array}\right],

then

\boldsymbol{A}^{\prime} \boldsymbol{A}

is equal to

Q7MathsUnit 3: Matrices and Determinants

The transpose of a column matrix is

Q8MathsUnit 3: Matrices and Determinants

A

is skew-symmetric, then

A^{n}

for

\boldsymbol{n} \in \boldsymbol{N}

is This question has multiple correct options

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