Unformatted text preview: 2 4 6.
1 2
0 0 0 0 0 0 3 6
01
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00 5 0
4 6 0 1 0 0 7 . Mark each statement T rue or False then justify y our answ er.
a. A homogeneous system of equations can be inconsistent.
b. If x is a nontrivial solution of Ax 0 , then every entry in x is nonzero.
c. T he effect of adding v ector p to a vector x is to move the vector x in a direction
parallel to p .
d. T he equation Ax b is homogeneous if the zero vector is a solution.
8 . If b 0 , can the solution set of Ax b be a plane through the origin? Explain. 2
9 . Construct a 3 3 nonzero matrix A such that the vector 1 is a solution of Ax 0 . 1 3 2 1 0 . G iven A 6 4 , find one nontrivial solution of Ax 0 by inspection. 12 8 1 1 . a. U se the original v ersion of the Gaussian Elimination A lgorithm to solve
.001 1 x1 1 . D o this w ith exact arithmetic.
1
2 x2 0 b. N ow employ the same algorithm on the same problem but simulate a t hree decimal digit
floating point environment (thus 2 1000 is computed as 1000 ).
c. F inally, use the same algorithm and do the w ork again in a t hree decimal digit floating
point environment (thus 1 .002 is computed as  1) but sw ap the tw o row s so you are 2 x1 0
1
solving .
.001 1 x2 1...
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 Spring '08
 PAVLOVIC
 Matrices, c. T, decimal digit, 3 40L

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