In the simplex method, we have occasion to compute the inverse of a matrix for which only one column is different from that of a matrix whose inverse if already known. Suppose that we have a non- singlar matrix B = (b1, b2, . bn) and that B-1 is known. Now we replace column r of B with a and wish to compute the inverse of Ba = (b1, b 2, br-1, a, br+1, . . ., bn). If the columns of B and Ba are viewed as two bases of En, then Ba is obtained from B by changing a single vector in the basis. Use this to derive the inverse of Ba as a function of B-1. B-1 = 204 516 793 where the second column of B is replaced by a random vector in R3 . You may read on elementary transformations, present the theory and write a code to generate the output.

Reduce the matrix -1 -2 -4 8. A 3= -1 -8 2 1 -4 ed row-echelon form. 9:45 9 Type here to search 口令 NG 3/18/ UPEEF (凸)

-Make a 3 x 4 matrix with rank equal to 1. -Make a 3 x 4 matrix with nullity equal to 1.

Show that if A is square matrix that satisfies the equation 2 A² - A - I = O, then its inverse is A-¹ = 2 A-I. The equation 24² - A - I = O implies that ---Select--- ✓. It follows that ---Select--- ✓. Notice the last equation means that ---Select--- multiplied with A is the identity, which is what we wanted to prove.