Unformatted text preview: 22702, LINEAR ALGEBRA 01/18/05
TRUE OR FALSE PROBLEMS IN CHAPTER 1 Determine Whether the following statement is True ofFaise. 1. A system of four linear equations in three unknowns is aiways inconsistent.
2. There exists a 3 x 4 matrix with rank 4. 3. If A is a 3 x 4 matrix and vector 17 is in R4? then vector A6 is in R3. 4. If the 4 x 4 matrix A has rank 4, then any linear system with coefﬁcient matrix A wiii have a unique soiution.
2 2 2 sum}; 222:2.
222 3
W1
6. There exists a matrix A such that A [ J = 6 .
7 2
1 4 7
7. Vector 2 is a linear combination of 5 and 8 .
3 6 9
a .—
8. if A is a nonzero matrix of the form then the rank of A must be 2.
b a 9. If A and B are matrices of the same size, then the formula rk(A+B) = rk(A)+rk(B) must hold.
1 10. If A is a 3 x 4 matrix of rank 3, then the system Ads“ = 2 must have inﬁniteiy 3
many solutions. Bate: January 17, .. ...
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 Spring '10
 smith
 Linear Algebra, Algebra

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