Question 1 (5 points): Let A be an 20 × 20 matrix. (a) Suppose that A has 20 pivot positions. Does the matrix A−1 exist? Explain your answer. (b) Suppose that the columns of A are linearly independent. How many pivot positions does A have? Explain your answer. (c) Suppose that the columns of A are linearly independent. For which vectors b is the equation Ax = b consistent? Explain your answer. (d) Suppose that A−1 exists. How many solutions are there of the equation Ax = b? Explain your answer? (e) Suppose that A has a free variable. Does A−1 exist? Explain your answer.

Which set of lengths could represent the sides of a triangle? a. 3, 7, 10 b. 4, 5, 10 c. 6, 8, 14 d. 12, 6, 7

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above

10x − 5y + 14 = 0 whats the answer pls