(1) Find the determinant of A
(2) Compute the rank of A
Let the set of vectors {v1, v2 , v3} be linearly independent. Determine whether the
following sets of vectors are linearly dependent or independent.
(1) {v1 + v2 , v2 + v3 , v3 + v1}
(2) {v1 − v2 , v2 − v3 , v3 − v1}
Write down a 3×3 matrix A so that if the vector v = (x, y, z) in R3 is
multiplied by A , the x and y coordinates of v are unchanged, but the z
coordinate becomes zero.
Consider a = (1,−1,0,0) , b = (0,1,−1,0) , and c = (0,0,1,−1) .
(1) Find the orthonormal vectors A, B, C by Gram-Schmidt operations from a, b,
and c.
(2) Show that {A, B, C} and {a, b, c} are bases for the space of vectors
perpendicular to d = (1,1,1,1) .
Find the least squares parabola for the data points {(1,2), (2,5), (3,7), (4,1)}.
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