Inverse matrix Quiz 1

Question 1

Ryan is a mathematician who devised a machine which gives the value of reciprocal of a matrix, he feeds $$\left( \begin{matrix}   7 & -2  \   3 & 5  \\end{matrix} ight)$$ as input. What do you think his output will be if the machine works fine?

Accepted Answer

$$\left( \begin{matrix}   \dfrac{5}{41} & \dfrac{2}{41}  \   \dfrac{-3}{41} & \dfrac{7}{41}  \\end{matrix} ight)$$

Answer

$$\left( \begin{matrix}   \dfrac{-7}{41} & \dfrac{2}{41}  \   \dfrac{3}{41} & \dfrac{5}{41}  \\end{matrix} ight)$$

Answer

$$\left( \begin{matrix}   \dfrac{-5}{41} & \dfrac{7}{41}  \   \dfrac{2}{41} & \dfrac{3}{41}  \\end{matrix} ight)$$

Answer

$$\left( \begin{matrix}   \dfrac{7}{41} & \dfrac{-2}{41}  \   \dfrac{3}{41} & \dfrac{5}{41}  \\end{matrix} ight)$$

Question 2

I want to find the general form for the inverse of a 2 by 2 matrix given as $$\left( \begin{matrix}   a & b  \   c & d  \\end{matrix} ight) $$. What can you devise as the formula for it?

Accepted Answer

$$\dfrac{1}{ad-bc}\left( \begin{matrix}   d & -b  \   -c & a  \\end{matrix} ight) $$

Answer

$$\dfrac{1}{ad-bc}\left( \begin{matrix}   b & -d  \   -c & a  \\end{matrix} ight) $$

Answer

$$\dfrac{1}{ad-bc}\left( \begin{matrix}   d & -c  \   -d & a  \\end{matrix} ight) $$

Answer

$$\dfrac{1}{ad-bc}\left( \begin{matrix}   a & -b  \   -c & d  \\end{matrix} ight) $$

Question 3

An electronic beat musician has decided to produce music in such a way that the next beat is the inverse of previous. If the last beat was saved as a 2 by 2 matrix $$\left( \begin{matrix}   4 & 7  \   2 & 6  \\end{matrix} ight)$$. What would the next beat look like?

Accepted Answer

$$\left( \begin{matrix}   \dfrac{2}{5} & \dfrac{7}{10}  \   \dfrac{1}{5} & \dfrac{3}{5}  \\end{matrix} ight)$$

Answer

$$\left( \begin{matrix}   \dfrac{4}{5} & \dfrac{7}{10}  \   \dfrac{1}{5} & \dfrac{3}{5}  \\end{matrix} ight)$$

Answer

$$\left( \begin{matrix}   \dfrac{2}{5} & \dfrac{7}{10}  \   \dfrac{2}{5} & \dfrac{3}{5}  \\end{matrix} ight)$$

Answer

$$\left( \begin{matrix}   \dfrac{2}{5} & \dfrac{7}{5}  \   \dfrac{1}{5} & \dfrac{3}{5}  \\end{matrix} ight)$$

Question 4

Howard has two matrices with you named A and B, with I as the unit matrix. If A is the inverse of the matrices, which of the following is correct?

Accepted Answer

$$AB=I=BA$$

Answer

$$AB=I
e BA$$

Answer

$$AB
e I
e BA$$

Answer

$$AB
e I=BA$$

Question 5

Data in a computer is stored as a matrix for a program. The program is used to find the inverse of a matrix. If the input by the user is  $$\left( \begin{matrix}   5 & 6  \   -1 & 2  \\end{matrix} ight)$$

Accepted Answer

$$\left( \begin{matrix}   \dfrac{1}{8} & \dfrac{-3}{8}  \   \dfrac{1}{16} & \dfrac{5}{16}  \\end{matrix} ight) $$

Answer

$$\left( \begin{matrix}   \dfrac{5}{8} & \dfrac{-3}{8}  \   \dfrac{1}{16} & \dfrac{1}{16}  \\end{matrix} ight) $$

Answer

$$\left( \begin{matrix}   \dfrac{1}{8} & \dfrac{-1}{8}  \   \dfrac{3}{16} & \dfrac{5}{16}  \\end{matrix} ight) $$

Answer

$$\left( \begin{matrix}   \dfrac{1}{8} & \dfrac{-3}{8}  \   \dfrac{-1}{16} & \dfrac{5}{16}  \\end{matrix} ight) $$