MTH 1230 -- Linear Algebra -- Fall 1997

Quiz #1

Solve the following system by Gaussian elimination in matrix form, with back substitution. Indicate for each step which row operation you use.
$\begin{displaymath} \matrix & x&+& y&+&2z &= 9 \\ &2x&+&4y&-&3z &= 1 \\ &3x&+&6y&-&5z &= 0 \endmatrix\end{displaymath}$
Consider the following system of linear equations:
$\begin{equation*} \begin{matrix} &x_1 &+3x_2 &-2x_3& &+4x_5& &= 5 \\ & & &-x_3 &+2x_4 & &+3x_6 &= 1 \\ & & & & &2x_5 &+x_6 &= 2\end{matrix}\end{equation*}$

Identify which variables are leading and which are free. Write down the general solution of the system.
Let:
$\begin{displaymath} A= \bmatrix 2 & 1\\ 1 & 1\endbmatrix, \qquad B= \bmatrix 2 & 3\\ 4 & 6\endbmatrix, \qquad C= \bmatrix -3 & 5 \endbmatrix .\end{displaymath}$
For each of the following, indicate whether the operation is possible, and, if it is, compute the result.

(a)
A+C=
(b)
3 A - 2 B =
(c)
A B=
(d)
A C=
(e)
C A=
(f)
A^-1 =
(g)
B^-1 =
(h)
C^-1 =

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Created by Alexandru Suciu, Mon Sep 29, 1997

http://www.math.neu.edu/~suciu/mth1230/1230f97.q1/index.html