Can you describe, step-by step, how to do this in layman\'s terms because I cann

Question

Can you describe, step-by step, how to do this in layman's terms because I cannot understand the formal math descriptions that well. Thanks Let f=(cos(x)^2) and g=(sin(x)^2). Which of the following lie in the space spanned by f and g? a) cos(2x) b) 3+x^2 c)1 d) sin(x) e) 0 How do I go about solving this? I've read that I have to use an equivalent statements theorem that says that: If A is an n x n matrix, the the following statements are equivalent. 1) Ax=b must be consistent for every n x 1 matrix b. 2) det(A) cannot = 0 However I do not know how to apply these conditions. Also, how would I use turn these vectors into a matrix? Another question.. what is the purpose of solving for whether or not a target vector (d) has a linear combination of a set of other vectors p1,p2,p3? Does that tell me if the target vector (d) spans the the vectors p1,p2,p3?

Explanation / Answer

just go through it ..will help you http://math.berkeley.edu/~teleman/math/RepThry.pdf

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