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Matrices, algebra of matrices, type of matrices Mock Test for JEE

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Part of Matrices and Determinants in JEE Main Mathematics.

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Q1MathsUnit 3: Matrices and Determinants
[000]\left[\begin{array}{lll}0 & 0 & 0\end{array}\right] is an example of
Q2MathsUnit 3: Matrices and Determinants
For any square matrix A,A+AT\boldsymbol{A}, \boldsymbol{A}+\boldsymbol{A}^{T} is
Q3MathsUnit 3: Matrices and Determinants
Assertion f[x1][10−23][x−5]=0,\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 xx is either- 3 or 5 Reason Two matrices [xyuv]\left[\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y} \\ \boldsymbol{u} & \boldsymbol{v}\end{array}\right] \& [abcd]\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 B\boldsymbol{B} is
Q5MathsUnit 3: Matrices and Determinants
A matrix consisting of a single column of m elements is know as
Q6MathsUnit 3: Matrices and Determinants
Choose the correct answer
Q7MathsUnit 3: Matrices and Determinants
matrix is a square matrix in which all the elements other than the principal diagonal elements are zero.
Q8MathsUnit 3: Matrices and Determinants
If AA is a skew symmetric matrix of order 3, then the value of ∣A∣|\boldsymbol{A}| is
Q9MathsUnit 3: Matrices and Determinants
Let A,B,C,DA, B, C, D be (not necessarily square) real matrices such that AT=\boldsymbol{A}^{\boldsymbol{T}}= BCD;BT=CDA;CT=DAB\boldsymbol{B} \boldsymbol{C} \boldsymbol{D} ; \boldsymbol{B}^{T}=\boldsymbol{C} \boldsymbol{D} \boldsymbol{A} ; \boldsymbol{C}^{T}=\boldsymbol{D} \boldsymbol{A} \boldsymbol{B} and DT=ABCD^{T}=A B C for the matrix S=ABCDS=A B C D, consider the two statements. S3=S\boldsymbol{S}^{3}=\boldsymbol{S} ∥S2=S4\| S^{2}=S^{4}
Q10MathsUnit 3: Matrices and Determinants
Suppose AA is any 3×33 \times 3 non-singular matrix and (A−3I)(A−5I)=O(\boldsymbol{A}-\mathbf{3} \boldsymbol{I})(\boldsymbol{A}-\mathbf{5} \boldsymbol{I})=\boldsymbol{O} where I=I3\boldsymbol{I}=\boldsymbol{I}_{3} and O=O3,\boldsymbol{O}=\boldsymbol{O}_{3}, If αA+\boldsymbol{\alpha} \boldsymbol{A}+ βA−1=4I,\beta A^{-1}=4 I, then α+β\alpha+\beta is equal to
Q11MathsUnit 3: Matrices and Determinants
If A=[−i00i],\boldsymbol{A}=\left[\begin{array}{cc}-\boldsymbol{i} & \mathbf{0} \\ \mathbf{0} & \boldsymbol{i}\end{array}\right], then A′A\boldsymbol{A}^{\prime} \boldsymbol{A} is equal to
Q12MathsUnit 3: Matrices and Determinants
The transpose of a column matrix is
Q13MathsUnit 3: Matrices and Determinants
If AA is skew-symmetric, then AnA^{n} for n∈N\boldsymbol{n} \in \boldsymbol{N} is This question has multiple correct options
Q14MathsUnit 3: Matrices and Determinants
Matrices obtained by changing rows and columns is called
Q15MathsUnit 3: Matrices and Determinants
Assertion Let⁡A=[a11a12a21a22],X=[x1x2],y=\operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a}_{11} & \boldsymbol{a}_{12} \\ \boldsymbol{a}_{21} & \boldsymbol{a}_{22}\end{array}\right], \boldsymbol{X}=\left[\begin{array}{l}\boldsymbol{x}_{1} \\ \boldsymbol{x}_{2}\end{array}\right], \boldsymbol{y}= [y1y2\left[\begin{array}{l}\boldsymbol{y}_{1} \\ \boldsymbol{y}_{2}\end{array}\right. If AA is symmetric, then X′AY=Y′AXX^{\prime} A Y=Y^{\prime} A X for each pair of XX and YY Reason If X′AY=Y′AX\boldsymbol{X}^{\prime} \boldsymbol{A} \boldsymbol{Y}=\boldsymbol{Y}^{\prime} \boldsymbol{A} \boldsymbol{X} for each pair of X\boldsymbol{X} and Y,Y, then AA is symmetric.

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