Quiz Chapter 04.01: Introduction to Matrix Algebra


(All Tests)


(More on Simultaneous Linear Equations)


(More on Simultaneous Linear Equations)

Pick the most appropriate answer

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 1/5th of its customers, while the rest switch to Imac. Each year, Imac keeps 1/3rd of its customers, while the rest switch to Dude. If in 2003, Dude had 1/6th of the market and Imac had 5/6th 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