tf1 - 2270-2 LINEAR ALGEBRA TRUE OR FALSE PROBLEMS IN...

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Unformatted text preview: 2270-2, 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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