Tag: business maths

Questions Related to business maths

If $A$ and $B$ are square matrices such that $B=-A^{-1}BA$, then 

business maths applications of matrices and determinants elementary transformations of a matrix multiplicative inverse of a matrix inverse of a matrix

  1. $AB+BA=0$

  2. $(A+B)^{o}=A^{2}+B^{2}$

  3. $(A+B)^{2}=A^{2}+2AB+B^{2}$

  4. $(A+B)^{2}=A+B$

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Correct Option: A

If $A$ is a $2\times 2$ matrix such that $A^{2}-4A+3I=0$, then the inverse of $A+3I$ is equal to

business maths applications of matrices and determinants elementary transformations of a matrix multiplicative inverse of a matrix inverse of a matrix

  1. $\dfrac{1}{24}S-\dfrac{7}{24}I$

  2. $\dfrac{1}{21} A-\dfrac{7}{21}I$

  3. $\dfrac{7}{24}I+\dfrac{1}{24}A$

  4. $A-3I$`

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Correct Option: A

If $A=\left[ \begin{matrix} 1 & -1 & 1 \ 2 & 1 & -3 \ 1 & 1 & 1 \end{matrix} \right] $ and $10B=\left[ \begin{matrix} 4 & 2 & 2 \ -5 & 0 & \alpha  \ 1 & -2 & 3 \end{matrix} \right] $ where $B=A^{-1}$ then $\alpha$ is equal to-

business maths applications of matrices and determinants elementary transformations of a matrix multiplicative inverse of a matrix inverse of a matrix

  1. $2$

  2. $-1$

  3. $-2$

  4. $5$

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Correct Option: A

The inverse of the matrix  $\left[ \begin{array} { c c c } { 1 } & { 0 } & { 0 } \ { 3 } & { 3 } & { 0 } \ { 5 } & { 2 } & { - 1 } \end{array} \right]$  is

business maths applications of matrices and determinants elementary transformations of a matrix multiplicative inverse of a matrix inverse of a matrix

  1. $- \dfrac { 1 } { 3 } \left[ \begin{array} { c c c } { - 3 } & { 0 } & { 0 } \ { 3 } & { 1 } & { 0 } \ { 9 } & { 2 } & { - 3 } \end{array} \right]$

  2. $- \dfrac { 1 } { 3 } \left[ \begin{array} { c c c } { - 3 } & { 0 } & { 0 } \ { 3 } & { - 1 } & { 0 } \ { - 9 } & { - 2 } & { 3 } \end{array} \right]$

  3. $- \dfrac { 1 } { 3 } \left[ \begin{array} { c c c } { 3 } & { 0 } & { 0 } \ { 3 } & { - 1 } & { 0 } \ { - 9 } & { - 2 } & { 3 } \end{array} \right]$

  4. $- \dfrac { 1 } { 3 } \left[ \begin{array} { c c c } { - 3 } & { 0 } & { 0 } \ { - 3 } & { - 1 } & { 0 } \ { - 9 } & { - 2 } & { 3 } \end{array} \right]$

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Correct Option: A

If $A=\left[ \begin{matrix} 1 & 0 & -1 \ 3 & 4 & 5 \ 0 & 6 & 7 \end{matrix} \right]$ and $A^{-1}=[\alpha _{ij}] _{3\times 3}$ then $\alpha _{23}=$

business maths applications of matrices and determinants elementary transformations of a matrix multiplicative inverse of a matrix inverse of a matrix

  1. $-1/5$

  2. $1/5$

  3. $-2/5$

  4. $2/5$

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Correct Option: A

Inverse of $\begin{bmatrix} -1 & 5 \ -3 & 2 \end{bmatrix}$ is

business maths applications of matrices and determinants elementary transformations of a matrix multiplicative inverse of a matrix inverse of a matrix

  1. $\begin{bmatrix} 2/13 & -5/13 \ 3/13 & -1/13 \end{bmatrix}$

  2. $\begin{bmatrix} -2/13 & 5/13 \ -3/13 & 1/13 \end{bmatrix}$

  3. $\begin{bmatrix} 2 & -5 \ 3 & -1 \end{bmatrix}$

  4. $Cannot\ be\ determined$

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Correct Option: A

If A is a 2 X 2 matrix such that $A^2009 + A^2008$= I, then : $(A^2008)^-1$= 

business maths applications of matrices and determinants elementary transformations of a matrix multiplicative inverse of a matrix inverse of a matrix

  1. $A^2008 + I$

  2. $A^2009 + 1$

  3. A + I

  4. A

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Correct Option: A

If $I=I=\left[ \begin{matrix} 1 \ 0 \end{matrix}\begin{matrix} 0 \ 1 \end{matrix} \right] ,j=\left[ \begin{matrix} 0 \ -1 \end{matrix}\begin{matrix} 1 \ 0 \end{matrix} \right] and B=\left[ \begin{matrix} cos\theta  \ -sin\theta  \end{matrix}\begin{matrix} sin\theta  \ cos\theta  \end{matrix} \right] ,$ then B =

business maths applications of matrices and determinants elementary transformations of a matrix multiplicative inverse of a matrix inverse of a matrix

  1. $Icos\theta +Jsin\theta $

  2. $Icos\theta -Jsin\theta $

  3. $Isin\theta +Jcos\theta $

  4. $-Icos\theta +Jsin\theta $

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Correct Option: A
Explanation:
Given, $I=\begin{bmatrix} 1 & 0\\ 0 & 1\end{bmatrix}, J=\begin{bmatrix} 0 & 1\\ -1 & 0\end{bmatrix}$

and $B=\begin{bmatrix} \cos \theta &\sin\theta \\ -\sin\theta & \cos\theta\end{bmatrix}$

$=\cos\theta\begin{bmatrix} 1 & 0\\ 0 & 1\end{bmatrix} +\sin\theta \begin{bmatrix} 0 & 1\\ -1 & 0\end{bmatrix}$

$=I\cos\theta +J\sin\theta$.

Let p be a non-singular matrix, $1+p+p^{2}+....+p^{n}=0$ (0 denotes the null matrix) then $p^{-1}=$

business maths applications of matrices and determinants elementary transformations of a matrix multiplicative inverse of a matrix inverse of a matrix

  1. $p^{n}$

  2. -$p^{n}$

  3. -(1+p+...+$p^{n}$)

  4. none

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Correct Option: A

Let A be a $3 \times 3$  matrix such that is: $A\left[ \begin{matrix} 1 & 2 & 3 \ 0 & 2 & 3 \ 0 & 1 & 1 \end{matrix} \right]=\left[ \begin{matrix} 0 & 0 & 1 \ 1 & 0 & 0 \ 0 & 1 & 0 \end{matrix} \right]  $Then $A^{-1}$ is

business maths applications of matrices and determinants elementary transformations of a matrix multiplicative inverse of a matrix inverse of a matrix

  1. $\left[ \begin{matrix} 0 & 1 & 3 \ 0 & 2 & 3 \ 1 & 1 & 1 \end{matrix} \right] $

  2. $\left[ \begin{matrix} 3 & 2 & 1 \ 3 & 2 & 0 \ 1 & 1 & 0 \end{matrix} \right] $

  3. $\left[ \begin{matrix} 1 & 2 & 3 \ 0 & 1 & 1 \ 0 & 2 & 3 \end{matrix} \right] $

  4. $\left[ \begin{matrix} 3 & 1 & 2 \ 3 & 0 & 2 \ 1 & 0 & 1 \end{matrix} \right] $

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Correct Option: A