Question

Due in 2 hr

(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 5 and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? Is vector u =[964,-71,4249, 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 (aij)sxs by ak ak1, akk.9] and use this notation if necessary. ii. Is vector v [21, 11,32, 23,-115, 141, 41, 92] in the row space of A? Justify your answer. (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 5 and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? Is vector u =[964,-71,4249, 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 (aij)sxs by ak ak1, akk.9] and use this notation if necessary. ii. Is vector v [21, 11,32, 23,-115, 141, 41, 92] in the row space of A? Justify your answer.

Answer 1

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