MATH 223 Study Guide - Midterm Guide: Orthogonal Matrix, Diagonal Matrix, Invertible Matrix
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You must show your work and explain your answers: [15 marks] consider the matrix equation ax = b with. There is an invertible matrix m so that. 0: [2 marks] what is rank(a), [4 marks] give the vector parametric form for the set of solutions to ax = b, [6 marks] give a basis for the row space of a. Give a basis for the column space of a. Give a basis for the null space of a: [2 marks] let a be the 4 5 matrix obtained by deleting the 5th column of a from a. What is the rank of a : [15 marks] let. Determine an orthonormal basis of eigenvectors and hence an orthogonal matrix q and a diagonal matrix d so that a = qdqt . You may nd it useful to know that 5 is an eigenvalue of a: [7 marks] determine the matrix a corresponding to the linear transformation from.
