MT2_Practice.pdf - MATH 232[2 1 1(a A triangle has vertices...

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MATH 232 1 [2] 1. (a) A triangle has vertices P 0 , P 1 and P 2 . What formula gives the area of the triangle? [2] (b) How can we determine if three vectors in R 3 lie in a plane? [4] (c) Find all unit vectors in the plane P = s (3 , 0 , 1)+ t (1 , - 1 , 1) , s, t R which are orthogonal to the vector w = (1 , 2 , 0) .
MATH 232 2 [2] 2. (a) Given the complex numbers z 1 = 2 - i z 2 = 3 + 2 i z 3 = - 1 + i Compute z 1 z 2 - z 3 • | z 2 /z 3 |
MATH 232 3 [3] 3. (a) What are the two conditions for a non-empty set of vectors S in R n to be a subspace [6] 4. Indicate wether the following statements are true or false. No explanation necessary. T/F If the linear system A x = b is consistent then the vector b is in the column space of A . T/F If a matrix A has eigenvalue λ = 0 then the linear system A x = 0 has infinitely many solutions. ? T/F The square matrices A and A T can have different eigenvalues. T/F If u × v = u × w for three non-zero vectors u , v , w then v = w . T/F If det ( A ) = 3 then det (4 A - I ) = 11 . T/F If det ( ABA ) = 0 and A is invertible then B cannot be singular.
MATH 232 4 5.