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Properties of Matrices and vectors

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Please show all work for attached problems.

1. Let A, and B be skew- symmetric matrices. Prove that AB is skew symmetric if and only if AB = -BA

2. IF possible find a vector u=(a,b,c) where a, b, c are not all zero so that "u" is orthogonal to both vectors: x= (1,2,1) and y = (1,-1,1)

The following are proof questions. The questions are being asked so that you can show the steps in "IF......then" type of statements.

3. If 3x^2 -ax+14>0, then a^2<168

4. If [ 3x + 2y =0 ]
[ ax - y = 1 ] has a solution then "a" does not equal to -(3/2).

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