BSc Sem III ATKT 2015 ATKT Math Ll Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 All questions are compulsory 2)For Q.1, Q.2. 0.3. attempt any one ich $ mks)from part (a). and any three Subquestions (each 4 mks)from
2. Q3 For Q.4 Attempt any three (each Smks)
3. Q1 (a) Attempt any one Find the inverse of the following matrix and wri product of elementary matrices
4. Q2 State Rank Nulity theorem for a linear transformation | where are veetor spaces over R and verify it for followingT: | Ix, =
5. Q1 (b) Attempt any three {Each 4]
6. Q1 Let E be an elementary matrix obtained by some on and an elementary matrix obtained by undo (or inverse) ERO of the same on |. Then prove that ts invertible
7. Q2 Consider the following matrix and ERO. Show that = A* where A’ IS the matrix obtained by performing the given ERO on A
8. Q3 Define row rank, column rank and find row rank and column rank of following
9. Q4 Define matrix associated with and find matrix with to following T:R? = (x, y) with By = {(1,0,0), (0,1,0), (1,1,1)} basis of IR? of main diagonal formed by vectors row by prove thay ving in Euclidean space in () and find proj projection of a vect ‘a matrix and reduce
10. Q4 Check the following vectors Define an orthogor

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