This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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....
View
Full
Document
 Spring '08
 Staff
 Linear Algebra, Algebra, Invertible matrix, corresponding augmented matrix, corresponding coefficient matrix

Click to edit the document details