Solve the problem.Suppose a nonhomogeneous system of 15 linear equations in 17 unknowns has a solution for all possible constants on the right side of the equation. Is it possible to find 3 nonzero solutions of the associated homogeneous system that are linearly independent? Explain.
What will be an ideal response?
No.
Since every nonhomogeneous equation Ax = b has a solution, Col A spans ?15. So Dim Col A = 15. By the Rank Theorem, dim Nul A = 17 - 15 = 2. So the associated homogeneous system does not have more than 2 linearly independent solutions.
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Find all the first order partial derivatives for the following function.f(x, y, z) = e(sin (x) + yz)
A. 
= e(sin (x) + yz); 
= ze(sin (x) + yz); 
= ye(sin (x) + yz)
B. 
= cos(x)e(sin (x) + yz); 
= e(sin (x) + yz); 
= e(sin (x) + yz)
C. 
= 
e(sin (x) + yz); 
= ze(sin (x) + yz); 
= ye(sin (x) + yz)
D. 
= cos(x) e(sin (x) + yz); 
= ze(sin (x) + yz); 
= ye(sin (x) + yz)
Forces F1 and F2 act at the same point. Find the resultant force F and its magnitude.F1 = 2i - 2j, F2 = 6i - 13j
A. F = 4i - 19j ; 
= 19.4164878
B. F = 8i - 15j ; 
= 17
C. F = 8i + 15j ; 
= 17
D. F = 4i + 19j ; 
= 19.4164878
Find the zeros (if any) of the rational function.
?
?
A. -2 B. 2 C. 8 D. -8 E. None
Evaluate the polynomial for the given value of x.-3x + 7 for x = 4
A. -19 B. -5 C. -24 D. 4