Chapter 1: Matrices and Determinants March 15, 2024 Maven Leave a Comment Welcome to the Chapter 1: Matrices and Determinants Name Email 1. If A is an invertible matrix of order 2 then $det(A^{-1})$ be equal to $det(A)$ $\frac{1}{det(A)}$ 1 0 None 2. If A is 3 x 3 matrix and $\left |A \right |=4$, then $\left | A^{-1} \right |$ is equal to $\frac{1}{4}$ $\frac{1}{16}$ 2 4 None 3. If A and B non-singular matrix then, which of the following is incorrect? $A^{2}=I$ implies $A^{-1}=A$ $I^{-1}=I$ $If AX = B$ then $X =B^{-1}A$ If A is square matrix of order 3 then $\left | adjA \right |=\left | A\right |^{2} $ None 4. Which of the following matrix has no inverse $\begin{pmatrix} -1 &1 \\ 1& -4 \end{pmatrix}$ $\begin{pmatrix} 2 &-1 \\ -4& 2 \end{pmatrix}$ $\begin{pmatrix} cosa &sina \\ -sina& cosa \end{pmatrix}$ $\begin{pmatrix} sina &sina \\ -cosa& cosa \end{pmatrix}$ None 5. The inventor of input - output analysis is Sir Francis Galton Fisher Prof. Wassily W. Leontief Arthur Caylay None 6. The inverse matrix of $\begin{pmatrix} 3 &1\\ 5& 2 \end{pmatrix}$ is $\begin{pmatrix} 2 &-1\\ -5& 3 \end{pmatrix}$ $\begin{pmatrix} -2 &5\\ 1& -3 \end{pmatrix}$ $\begin{pmatrix} 3 &-1\\ -5& -3 \end{pmatrix}$ $\begin{pmatrix} -3 &5\\ 1& -2 \end{pmatrix}$ None 7. If A= $\begin{pmatrix} -1 &2\\ 1& -4 \end{pmatrix}, then A(adjA)$ is $\begin{pmatrix} -4 &-2\\ -1& -1 \end{pmatrix}$ $\begin{pmatrix} 4 &-2\\ -1& 1 \end{pmatrix}$ $\begin{pmatrix} 2 &0\\ 0& 2 \end{pmatrix}$ $\begin{pmatrix} 0 &2\\ 2& 0 \end{pmatrix}$ None 8. If A is a square matrix of order 3 and $\left |A \right |=3$, then $\left |adjA \right |$ = 81 27 3 9 None 9. The value of $\begin{vmatrix} x & x^{2}-yz & 1\\ y & y^{2}-zx &1 \\ z & z^{2}-xy & 1 \end{vmatrix}$ is 1 0 -1 -xyz None 10. The value of $\begin{vmatrix} 5 & 5 & 5\\ 4x & 4y &4z \\ -3x& -3y & -3z \end{vmatrix}$ is 5 4 0 -3 None 11. If $\begin{vmatrix} x & 2\\ 8 & 5 \end{vmatrix} =0$, then the value of x is $-\frac{5}{6}$ $\frac{5}{6}$ $-\frac{16}{5}$ $\frac{16}{5}$ None 12. If A =$\begin{bmatrix} cos\theta &sin\theta \\ -sin\theta & cos\theta \end{bmatrix}$ then $\left | 2A \right |$is equal to $4cos2\theta$ 4 2 1 None 13. If $\Delta \begin{vmatrix} a_{11} &a_{12} &a_{13} \\ a_{21} &a_{22} & a_{23}\\ a_{31} &a_{32} & a_{33} \end{vmatrix} and A_{ij}$ is a cofactor of $a^{ij}$ then the value of $\Delta$ is given by $a^{11}A^{31}+a^{12}A^{32}+a^{13}A^{33}$ $a^{11}A^{11}+a^{12}A^{21}+a^{13}A^{31}$ $a^{21}A^{11}+a^{22}A^{12}+a^{23}A^{13}$ $a^{11}A^{11}+a^{21}A^{21}+a^{31}A^{31}$ None 14. If $\begin{vmatrix} 4 & 3\\ 3 & 1 \end{vmatrix} =-5$ then the value of $\begin{vmatrix} 20 & 15\\ 15 & 5 \end{vmatrix}$ is -5 -125 -25 0 None 15. If any three rows or columns of a determinant are identical then the value of the determinant is 0 2 1 3 None 16. The inverse matrix of $\begin{pmatrix} \frac{4}{5} &\frac{-5}{12} \\[7pt] \frac{-2}{5}& \frac{1}{2} \end{pmatrix}$ is $\frac{7}{30}\begin{pmatrix} \frac{1}{2} &\frac{5}{12} \\[7pt] \frac{2}{5}& \frac{4}{5} \end{pmatrix}$ $\frac{7}{30}\begin{pmatrix} \frac{1}{2} &\frac{-5}{12} \\[7pt] \frac{-2}{5}& \frac{1}{5} \end{pmatrix}$ $\frac{30}{7}\begin{pmatrix} \frac{1}{2} &\frac{5}{12} \\[7pt] \frac{2}{5}& \frac{4}{5} \end{pmatrix}$ $\frac{30}{7}\begin{pmatrix} \frac{1}{2} &\frac{-5}{12} \\[7pt] \frac{-2}{5}& \frac{4}{5} \end{pmatrix}$ None 17. The value of the determinant $\begin{vmatrix} a & 0 & 0\\ 0 & b & 0\\ 0 & 0 & c \end{vmatrix} ^{2}$ is abc 0 $a^{2}b^{2}c^{2}$ -abc None 18. The value of $\begin{vmatrix} 2x+y &x &y \\ 2y+z&y &z\\ 2z+x & z & x \end{vmatrix}$ is x y z x + y + z 2x + 2y + 2z 0 None 19. The value of x if $\begin{vmatrix} 0 &1 &0 \\ x&2 &x \\ 1 & 3 & x \end{vmatrix} =0$ is 0, –1 0, 1 –1, 1 –1, –1 None 20. If A =$\begin{pmatrix} a & b \\ c& d \end{pmatrix}$ such that $ad-bc\neq 0$, then $A^{-1}$ is $\frac{1}{ad-bc}\begin{pmatrix} d & b\\ -c& a \end{pmatrix}$ $\frac{1}{ad-bc}\begin{pmatrix} d & b\\ c& a \end{pmatrix}$ $\frac{1}{ad-bc}\begin{pmatrix} d & -b\\ -c& a \end{pmatrix}$ $\frac{1}{ad-bc}\begin{pmatrix} d & -b\\ c& a \end{pmatrix}$ None 21. The number of Hawkins- Simon conditions for the viability of an input-output analysis is 1 3 4 2 None 22. The cofactor of –7 in the determinant $\begin{vmatrix} 2 &-3 &5 \\ 6&0 &4\\ 1 & 5 & -7 \end{vmatrix}$ is -18 18 -7 7 None 23. adj (AB) is equal to adjA adjB $adjA^{T}adjB^{T}$ adjB adjA $adjB^{T}adjA^{T}$ None 24. If A is square matrix of order 3 then $\left | ka \right |$ is k$\left | a \right |$ -k$\left | a \right |$ $k^{3}\left | a \right |$ -$k^{3}\left | a \right |$ None 25. If $\Delta =\begin{vmatrix} 1 & 2 & 3\\ 3 & 1 & 2\\ 2 & 3 & 1 \end{vmatrix}$ then $\begin{vmatrix} 3 & 1 & 2\\ 1 & 2 & 3\\ 2 & 3 & 1 \end{vmatrix}$ is $\Delta$ -$\Delta$ 3$\Delta$ -3$\Delta$ None Time's up Related Posts:Chapter 1: Applications of Matrices and DeterminantsChapter 4: Cost and Revenue AnalysisChapter 5: Market Structure and PricingChapter 8: Indian Economy Before and After Independence
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