What are the dimensions of A? (ii) (8 pts.) Determine the three columns a), a(2) and...

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What are the dimensions of A? (ii) (8 pts.) Determine the three columns a), a(2) and a) of A (and thus A itself). Hint: Sum both sides of the last two equalities. (iii) (4 pts.) In the usual three-dimensional Cartesian space (with orthogonal axes), consider the plane S which contains the origin and has normal vector [111]. Determine the reflection of the point [100] about S. (Hint: Express [100]" as a sum of two vectors, one parallel to [111] and one orthogonal to it.) (iv) (4 pts.) By symmetry, determine the reflections of [010] and [0 0 1] about S. Explain why the matrix A represents a reflection of an arbitrary point (in three-dimensional space) about S. (v) (3 pts.) Study the function TOEPLITZ in MATLAB documentation. Give a single row vector c such that A toeplitz (c) produces the matrix A of parts (1)-(iv) above. E-8 - H-G [FIE Let What are the dimensions of A? (ii) (8 pts.) Determine the three columns a), a(2) and a) of A (and thus A itself). Hint: Sum both sides of the last two equalities. (iii) (4 pts.) In the usual three-dimensional Cartesian space (with orthogonal axes), consider the plane S which contains the origin and has normal vector [111]. Determine the reflection of the point [100] about S. (Hint: Express [100]" as a sum of two vectors, one parallel to [111] and one orthogonal to it.) (iv) (4 pts.) By symmetry, determine the reflections of [010] and [0 0 1] about S. Explain why the matrix A represents a reflection of an arbitrary point (in three-dimensional space) about S. (v) (3 pts.) Study the function TOEPLITZ in MATLAB documentation. Give a single row vector c such that A toeplitz (c) produces the matrix A of parts (1)-(iv) above. E-8 - H-G [FIE Let

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A Toeplitz matrix is a matrix where each descending diagonal from left to right is constant In other ... View the full answer