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Unformatted text preview: x 1x 2 = 1 x 1 + kx 24 x 3 = 3x 1 + 2 x 2(1 + k ) x 3 = 0 have (a) inﬁnitely many solutions? (b) no solutions? (c) exactly one solution? Justify your answers and provide a brief geometric interpretation. 4 (3) Find the matrix A of the orthogonal projection onto the plane x 1x 2 + x 3 = 0 . Describe geometrically the transformation given by A 2 . Is A invertible? 5 (4) Find the inverse of the matrix A = 1 1 4 1 2 3 1 6 (5) Determine whether the following statements are true or false. No explanations, no credit. (a) Given two square matrices A and B , if AB is invertible, then so is A . (b) The composition of a shear, a reﬂection and a rotation in the plane is invertible. (c) There exist matrices A of size 3 × 2 and B of size 2 × 3 such that AB = I 3 is the identity matrix....
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 Spring '08
 Staff
 Linear Algebra, Algebra, Invertible matrix, corresponding augmented matrix, corresponding coefficient matrix

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