PT 3

Which of the vectors below is orthogonal to both (2, 1, -1) and (-3, -2, 4)?

• (-6,-2,-4)

• (2, -5, -1)

• (-2, 5, 1)

• (2, 5, 1)

Let u = (1, 2, 1); v = (2, 3, 0); w = (0, 1, 0). Find projection of u x v on w.

• (0, 0, 0)

• (2, 0, 0)

• (0, 2, 0)

• (0, 0,2)

Let u = (3, 3, 6), v = (4, 4, 3), w = (-6, 3, 3) and x = (41, 5, 12).

We can write x = au + bv + cw,where a, b, c are numbers. Find b.

• 1

• 2

• 3

• 4

Which of the following are subspaces of R3?

(i) {(x, y, z)| 2x-y+3z=0}

(ii) (x, y, z)| xy=0}

• (i)+(ii)

• (i)

• (ii)

• None of the other choices is correct

Find the dimension of the subspace U = {[x, y, z, t] | x+4y-z = 0; x-2z+ t= 0}.

• 1

• 3

• 2

• None of the other choices is correct

Find the dimension of the subspace

H = { [a+2b+2d, c+d, -3a-6b+4c-2d, -c-d] | a, b, c, d in R}

• H=1

• H=4

• H=3

• H=2

Let A be 4 x 7 matrix that has dim(Null(A)) = 5. Choose the correct statements:

(i) A has exactly 5 independent columns

(ii) A has exactly 2 independent rows

• (i)

• (i)+(ii)

• (ii)

• None of the other choices is correct

Let u = (2; 1; 2) and v = (-1; 0; 1). Find x such that

3u + 7v =|| u || (2x+v)

• x=(3/6; 2/6; 10/6)

• x=(3/6; 3/6; 10/6)

• x=(2/6; 3/6; 10/6)

• x=(2/6; 3/6; 6/10)

Find the number a such that the set {[1 2 1 0]T, [1 -1 1 3]T, [2 -1 0 -1]T, [a b c 1]T } is orthogonal.

• 1

• -3

• 2

• -2

Let U = {[x, y, z]| x - 2y + z = 0, x + y - z = 0}. Which of the following is a basis for U?

• {[2, 2, 3]}

• {[1, 2, 3]}

• {[1, 3, 3]}

• {[1, 1, 3]}