Question

even though DE These strange results actually pertain only to the special class of matrices known singular matrices, of which the matrices A, B, and C are examples. (Roughly, these matr ccs contain a row which is a multiple of another row.) Neverthcless, such examples d reveal the pitfalls of unwarranted extension of algcbraic theorems to matrix opcrations. ERCISE 4.5 Given A =-1 S 71. , and x-1X1 0-2 41,- 1. Calculate: (a) A (b A () ix (d) x Indicate the dimension of the identity matrix used in each case. Chapter 4 Lineur Medels and Matrix Algehva 73 2. Calculate: (a) Ab (b) Alb )IA (d) xA Does the insertion of i in (b) affect the result in (a)? Does the deletion of l in (d) affect the result in ()? 3. What is the dimension of the null matrix resulting from each of the foilowing? (o) Premultiply A by a 5 x 2 null matrix. (b) Postmultiply A by a 3 x 6 null matrix. (c) Premultiply b by a 2 × 3 null matrix. (d) Postmultiply x by a 1 x 5 null matrix. 4. Show that the diagonal matrix 011 00

Answer 1

Step by step solution is provided in the pic attached here.

If you have any doubt , feel free to ask.

Don't forget to thumbs up , if you like the solution.

A = [- 1 0 5 - 2 7 4] ib = [9 6 0] & x = [x_1 x_2] (a) let 1 be a 3 times 3 matrix AI = [- 1 0 5 - 2 7 4] [1 0 0 0 1 0 0 0 1] = [- 1 0 5 - 2 7 4] (b) I rightarrow 3 times 3 matrix IA = [1 0 0 0 1 0 0 0 1] [- 1 0 5 - 2 7 4] = [- 1 0 5 - 2 7 4] (c) Iy 2 times 2 matrix Ix = [1 0 0 1] [x_1 x_2] = [x_1 x_2] (d) x' = [x_1 x_2] let Iy 2 times 2 matrix x' I = [x_1 x_2] [1 0 0 1] = [x_1 x_2] (a) Ab = [- 1 0 5 - 2 7 4] [9 6 0] = [- 9 + 30 + 0 0 - 12 + 0] = [21 - 12]