MATH 235 Midterm: MATH 235 UMass Amherst midterm2-spring01

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turquoisegnu128

31 Jan 2019

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Spring 2001: (24 points) you are given below the matrix a together with its row reduced echelon form b. 0: is the vector, (16 points) let a = answer! Compute i) a 1, ii) b 1, and iii) (ab) 1. Check your answers in parts i and ii by calculating aa 1 and bb 1: (16 points) a) let a, b and c be 4 4 matrices satisfying. B = aca 1 + 2a, with a invertible. Solve for c in terms of a and b: let a = (cid:20) 1 2. 2 5 (cid:21) and c = (cid:20) 1 2. Find a matrix b satisfying ab = c. 3: check your answer in part b by calculating ab, (18 points) determine which of the following sets in rn is a subspace. Nd a property in the de nition of a subspace which this set violates.

Related Questions

4. (12 points) Let the matrix A and its reduced row echelon form R be given by the following. A= [ 1 -2 2 -3 1 -2 4 -1 4 1 -3] [1001 1] -4 0 0 1 0 1 1 7 -1 0 0 1 1 -1 | = R. (a) Find a basis for the column space of A. (b) Find a basis for the row space of A. (c) Find a basis for the null space of A. (d) Verify that the dimension of the column space of A plus the dimension of the null space of A is equal to the number of columns of A.

(10] 1. Given that /1 0 2 1 -1 2 0 3 0 1 A4 07 2-1 0 0 1 3 1 / has reduced row echelon form R= (1 000 17 0 0 1 0 -11 0001 4: OOOOO find a basis for each of the following: (a) The row space of A. (b) The column space of A. (c) The null space of A.

Show procedure please! thanks!