CS972: Assignment 2
May, 2023
Time: 10 days Maximum Marks: 50Machine Learning Assignment 2 
Question (5 + 5 + 10 + 15 + 15 marks). Consider the matrix
A =  3 2 1 2 1 0 0 1 1  .
1. Do Gaussian elimination on A to convert A into an upper triangular matrix. Show
matrices obtained after each step of Gaussian elimination.
2. Do Gaussian elimination on A to convert A into a lower triangular matrix. Show
matrices obtained after each step of Gaussian elimination.
3. For which numbers c and d, the matrix B is of rank 2 where
B =  1 2 5 0 5 0 0 0 0 0c d2 22  .
4. Compute all eigenvalues and eigenvectors of matrix C where
C =  0 0 2 0 2 0 2 0 0  .
5. Let V be the real vector space spanned by the rows of the matrix A, where
A =

3 21 0 9 0
1 7 –1 –2 –1
2 14 0 6 1
6 42 –1 13 0

.
Find the basis for V . Tell which vectors (x1, x2, x3, x4, x5) are elements of V .
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