could you answer these 4 questions. show the steps please.
Consider the three vectors (1, 3, 2), (-4, -2, 5), (19, -13, 10) Show they are mutually orthogonal. (Show all the work.) Find values of a, b, and c such that (Show all the work.) a(1, 3, 2) + b (-4, -2, 5) + c (19, -13, 10) = (23, 17, -45). a (1, 3, 2) + b (-4, -2, 5)+c (19, -13, 10) = (7, 21, -17) a(1, 3, 2) + b (-4, -2, 5) + c (19, -13, 10) = (8, -3, 7) Using the same approach to give the values of a, b, c, and d such that a (1, 2, 6, 2) + b (2, 1, -1, 1) + c (8, -10, 3, -3) + d (8, 16, 3, -29) = (7, 21, -17, 33) a (2, 3, 2, -2) + b (1, 0, 0, 1) + c (-1, 0, 2, 1) + d (-1, 2, -1, 1) = (13, 6, 9, 11) As an illustration of where this approach does not work, solve for a, b, c by this same method on a (2, 3, 2, -2) + b (1, 0, 0, 1) + c (-1, 0, 2, 1) = (13, 6, 9, 11) (Clearly, you should get the same three values as on the last problem.) Once you get those values of a, b, c calculate the value of a (2, 3, 2, -2) + b (1, 0, 0, 1) + c (-1, 0, 2, 1) and compare it to (13, 6, 9, 11). Are they the same? Let C [- 1,1] be the set of continuous functions on the interval [- 1, 1]. For f,g epsilon C [-1, 1], define What are the values of (Again, show ALL the steps. Give decimals to the thousandths.) (1,cosx) (x2 + x + 1,x - 3) (sin x, cos x) (x, sinx) Characterize all the functions ax2 + bx + c for which (ax2 + bx + c, x2 + l) = 0. The final answer will be some equation involving a, b and c. Give two examples of such functions.