MTH 1230 - Linear Algebra - Fall 1997

Quiz 1

Problem 1

Solve the following system by Gaussian elimination in matrix form, with 
back substitution.  Indicate for each step which row operation you use.

Solve[{x+y+2z == 9,2x+4y-3z == 1,3x+6y-5z == 0},{x,y,z}]

Problem 2

Consider the following system of linear equations.  Identify which variables 
are leading and which are free. Write down the general solution of the system.

Solve[{x[1]+3x[2]-2x[3]+4x[5]==5,-x[3]+2x[4]+3x[6]==1,
2x[5]+x[6]==2},Table[x[i],{i,6}]]

Problem 3

For each of the following matrices, indicate whether the operation is possible, 
and, if it is, compute the result.

a={{2,1},{1,1}}; b={{2,3},{4,6}}; c={{-3,5}};

a+c

3*a-2*b

a.b

a.c

c.a

Inverse[a]

Inverse[b]

Inverse[c]