Download Linear Algebra Homework #1 Due 10/2 6:20 pm From textbook, ed

Linear Algebra Homework #1
Due 10/2 6:20 pm
From textbook, ed. 6
1. p.11, exercise 10
Find a parametric representation of the solution set of
13x1  26 x2  39 x3  13.
2. p.11, exercise 20
Graph the following system of equation as a pair lines in the xy-plane. Solve it and
interpret your answer.
1
1
x  y 1
2
3
4
2 x  y   4
3
3. p.12, exercise 56
Solve the following system of linear equation.
x1 
3 x4  4
2 x2  x3  x4  0
3 x2 
2 x4  1
2 x1  x2  4 x3  5
4. p.13, exercise 86
Find the values of a, b, an dc such that the system of linear equation has (a) exactly
one solution , (b) an infinite number of solutions and (c) no solution.
x  5y  z  0
x  6y  z  0
2 x  ay  bz  c
5. p.14, exercise 94
In Figure 1, the graphs of two equations are shown and appear to be parallel. Solve
the system of equations algebraically. Explain why the graphs are misleading.
Figure 1
1
6. p.26, exercise 20
Find the solution set of the system of linear equations represented by the augmented
matrix
2 1 1 0 
1 2 1 2 


1 0 1 0 
7. p.26, exercise 36
Solve the system using both Gaussian elimination with back substitution or
Gauss-Jordan elimination.
2 x  y  z  2w  6
3x  4 y 
w 1
2 x  5 y  2 z  6w  3
5x  2 y  z  w  3
8. p.27, exercise 48
 2 1 3 
Consider the matrix A   4 2 k  .
 4 2 6 
(a) If A is the augmented matrix of a system of linear equations, determine the
number the number of equations and the number of variables.
(b) If A is the the augmented matrix of a system of linear equations, find the value(s)
of k such that the system is consistent.
(c) If A is the coefficient matrix of a homogeneous system of linear equations,
determine the number of equations and the number of variables.
(d) If A is the coefficient matrix of a homogeneous system of linear equations, find
the value(s) of k such that the system is consistent.
9. p.38, exercise 6
(a) Determine the polynomial function whose graph passes through the given points
(2005, 150), (2006, 180), 2007, 240), (2008, 260)
(b) Sketch the graph of the polynomial function, showing the given points.
10. p.40, exercise 28
Determine the currents I1, I2, I3, I4, I5, and I6 of for
the electrical network shown in Figure 2.
2