5) Determine a matrix whose null space consists of vectors that can be written as a...

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5) Determine a matrix whose null space consists of vectors that can be written as a linear combination of the vectors (1,0, -1) and (1, 1, 1). [3] 6) Determine a standard matrix for the transformation T: R³ → R³ that orthogonally projects a vector = (x, y, 2) onto the yz-plane. [3] 7) Determine the dimension of the space of all symmetric 3 x 3 matrices. [3] 5) Determine a matrix whose null space consists of vectors that can be written as a linear combination of the vectors (1,0, -1) and (1, 1, 1). [3] 6) Determine a standard matrix for the transformation T: R³ → R³ that orthogonally projects a vector = (x, y, 2) onto the yz-plane. [3] 7) Determine the dimension of the space of all symmetric 3 x 3 matrices. [3]