1 1 0. 1 , v2 = 1 be four vectors satisfying vector equation with Let vi = ,V3 = 1 unknowns xı, x2, X3, X4. X, V, +X, V2 +X; V3 +x, V, =0 (a) Determine if {v1, v2, v3, v4} forms a linearly independent set. Is it possible to find x1, x2, X3, X4 which satisfy the equation where at least one of x's is nonzero. If so give an example. (b) (c) Is it possible to find a vector b = such that no combinations of all x's satisfy a X, V, + X, V, + X; V, +x, v, =b except for a special value of a. If so, compute the value of this a. (d) For the vector b defined in (c), which value(s) of a is the vector v in Span {v2, V3 ,V4, b}? Explain.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.