a) For the vector space
a) For the vector space ℝ³ (3-dimensional Euclidean space), the basis vectors are typically represented as:
1. The first basis vector, e₁, is (1, 0, 0).
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a) Check whether the matrices
a) For the vector space
a) Consider the following system of equations:
Find the vector equation of the plane determined by the points (1, 0,−1), (0, 1, 1) and (−1, 1, 0). Also find the point of intersection of the line
a) Which of the following are subspaces of R3 ? Justify your answer.
i) { }
ii) { }
For those subsets which are subspaces, find a basis.
b) Check that
Which of the following statements are true and which are false? Justify your answer with a short proof or a counterexample.
i) The Row Reduced Echelon form of any invertible square matrix is the identity matrix
dim(W1) dim(v)/2,dim(W2)
dim(v) /2 ,the W1 ∩ W2
{0}.
iii) If
a) Let