CS972: Assignment 2

CS972: Assignment 2

CS972: Assignment 2
May, 2023
Time: 10 days Maximum Marks: 50
Question (5 + 5 + 10 + 15 + 15 marks). Consider the matrix
.
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
.
4. Compute all eigenvalues and eigenvectors of matrix C where
.
5. Let V be the real vector space spanned by the rows of the matrix A, where
?3
A = ??1
?2
6 21 7
14
42 0
-1
0
-1 9
-2
6 13 0 ?
-1?
1 ??.
0
Find the basis for V . Tell which vectors (x1,x2,x3,x4,x5) are elements of V .
1

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