M340L Midterm Exam
September 16, 1993
Problem 1: Find all solutions to the following system of equations:
x1+x2+x3−3x4=6
2x1+ 3x2−x3−4x4=11
x1−x2+x3−x4=2
x1−x2−x3+x4=0
Problem 2
a) Is the matrix A=
1 6 3
1 5 2
0 2 1
singular or non-singular? If Ais non-singular, find A−1.
b) Find all solutions to AX =B, where Ais given above and B=
1
−1
3
. (Hint: Use
the result of part a)
Problem 3. By doing row operations, put these matrices in reduced row-echelon form:
a)
1 2 1 4 3
2 4 3 6 5
−1−2 0 2 12
b)
0 2 4
−2 0 2
3 4 5
1 2 3
Problem 4. Evaluate the following determinants:
a)
3 5
7 12
b)
1 3 2
−1 1 5
2−2 4
Problem 5. True of False
a) If Ais a 3 ×5 matrix that has rank 3, then the equation AX =Bhas at least one
solution, regardless of what Bis.
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