MATH 1104 Midterm: MATH 1104 Term Test 2 2017 Fall

• School: Carleton University
• Department: Mathematics
• Course: MATH 1104
• Professor: All

Document Summary

Student no: [3 marks]: let a be a 4 7 matrix such that dim(cola = 4). What is dim(nul a), (dimension of the solution space for ax = 0)? (a) 1 (c) 3. 3 (f ) none: [5 marks]: find a value of k such that the given vectors are linearly dependent x1 = = 40 + 10k = 0 = k = 4 k. 3 reduce the matrix [x1 x2 x3] to ref, then nd k such that at least. In this case an ref form of is. An alternative way: one column of the reduced matrix is not leading column. Put 10k + 40 = 0 = k = 4. 10k + 40: [5 marks]: determine wether the following vectors are linearly independent or dependent. = 9 4 6 (cid:54)= 0 = the vectors are linearly independent. x1 = Alternatively: let a = [x1x2x3], then the only solution to ac = 0, is zero vector.