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4. Assorted true and false statements. Mark as T(true) or F(false).

____1. Vectors u = (4,1,2,5) and v = (1,5,8,1) are orthogonal.

____2. If A and B are 3x3 matrices, then det(A+ B) = det(A) + det(B) .

____3. The set of vectors (x, y) in 2 R with y = 2x +1 is a subspace of 2 R .

____4. If

1 2

,

2 3

spans R^2 , then

1 2 2

, ,

2 3 3

also spans R^2.

____5. If each component of a vector in 3 R is doubled, the norm of that vector is doubled.

____6. The set W of all solutions to a consistent system Ax = 0when A is mxn is a subspace of R^n .

____7. An elementary row operation can change det(A) from nonzero to zero.

____8. The intersection of two subspaces of a vector space V is a subspace of V.