# Quiz Chapter 04.01: Introduction to Matrix Algebra

 MULTIPLE CHOICE TEST BACKGROUND SIMULTANEOUS LINEAR EQUATIONS

1. Given $\begin{bmatrix}6&2&3&9 \\ 0&1&2&3 \\ 0&0&4&5 \\ 0&0&0&6 \end{bmatrix}$ then $\left[ A \right]$ is a(n) _____ matrix.

2. A square matrix $\left[ A \right]$ is lower triangular if

3. Given $\left[ A \right] = \begin{bmatrix} 12.3&-12.3&20.3 \\ 11.3&-10.3&-11.3 \\ 10.3&-11.3&-12.3 \\ \end{bmatrix}$, $\left[ B \right] = \begin{bmatrix} 2&4 \\ -5&6 \\ 11&-20 \\ \end{bmatrix}$ then if $\left[ C \right] = \left[ A \right] \left[ B \right]$, then $c_{31}=$ _____

4. The following system of equations has _____ solution(s).

• $x + y = 2$
• $6x+6y=12$

5. Consider there are only two computer companies in a country. The companies are named Dude and Imac. Each year, Dude keeps $1/5$th of its customers, while the rest switch to Imac. Each year, Imac keeps $1/3$rd of its customers, while the rest switch to Dude. If in 2003, Dude had $1/6$th of the market and Imac had $5/6$th of the market, what will be the share of Dude computers when the market becomes stable?

6. Three kids – Jim, Corey, and David – receive an inheritance of $\ 2,253,453$. The money is put in three trusts but is not divided equally to begin with. Corey’s trust is three times that of David’s because Corey made and $A$ in Dr. Kaw’s class. Each trust is put in an interest generating investment. The three trusts of Jim, Corey and David pays an interest of $6%$, $8%$, and $11%$, respectively. The total interest of all the three trusts combined at the end of the first year is $\ 190,740.57$. The equations to find the trust money of Jim $\left( J \right)$, Corey $\left( C \right)$, and David $\left( D \right)$ in a matrix form is