Question

please answer 2a(i) only

2. (a) Use Octave as a Calculator to answer this question. Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j - 1. The (i,j)-entry of the matrix A equals 0 if i +j is divisible by and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? ii. Is vector u- [9, 64,-71,42,49, 59,234,-196, 97] in the row space of A? If yes, write u as a suitable linear combination of the rows of A (rounding coefficients to two decimal places). Here, denote the k-th row of A (aj)8x9 iii Is vector v21, 11,32,23, -115, 141,41,92] in the row space of A? Justify (b) Let D be a mx n matrix. Show that every vector in null(D) is orthogonal to every by ak := [ak,l, ak,2, , ak,9] and use this notation if necessary. your answer vector in row(D). For k e (1,2,.., m] you may denote the k-th row of D by dkdki, dk 2,....dkn] (dij)mxn

Answer 1

2a)1) 8 13 5 1 13 15, 11 2 万 il 14 11 20 23 26 3 7 5 11 37 31 35 千914-19 a4ag 34-37 4t 511 17 2329 3ケ414753 Ç 13 20 27 3441 4g 55 62 7 15 3 3 24 47 55 63 71 005 I2 22 22 2 2 2 2 333 3 333 3 455 55sS 5 6 6 666 6 6 6

4-914-19 009 34-3744 511 17 O 2935-41470 С 13 О 27 34 41 48 062 7 O 23 31 29 41 0 63 7) Rank CAD = 8 Nulty CA1