This question concerns the following two subsets of R4: S={(1,0,0,2), (0, 1, 1, 0), (1, 1,...

 

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This question concerns the following two subsets of R4: S={(1,0,0,2), (0, 1, 1, 0), (1, 1, 0, 1)}, T= {(x, y, z, 2r-y+ z): x, y, z ER}. (a) Show that SCT, and write down a vector in R4 that does not belong to T, justifying your answer. (b) Show that T is a subspace of R4. (c) Show that S is a basis for T, and state the dimension of T. (d) Show that two of the vectors in S are orthogonal, and hence find an orthogonal basis for T. (e) Find an expression for the vector (1,3,-2.-3) in T as a linear combination of the vectors in your orthogonal basis for T. This question concerns the following two subsets of R4: S={(1,0,0,2), (0, 1, 1, 0), (1, 1, 0, 1)}, T= {(x, y, z, 2r-y+ z): x, y, z ER}. (a) Show that SCT, and write down a vector in R4 that does not belong to T, justifying your answer. (b) Show that T is a subspace of R4. (c) Show that S is a basis for T, and state the dimension of T. (d) Show that two of the vectors in S are orthogonal, and hence find an orthogonal basis for T. (e) Find an expression for the vector (1,3,-2.-3) in T as a linear combination of the vectors in your orthogonal basis for T.