MTH501 latest Subjective Questions Final term Spring 2011

Question of 2 Marks

1. Determine whether the set of vectors are orthogonal or not
2. Is following set of vertices is orthogonal with respect to the Euclidean inner product on ?




3. Find the characteristics polynomial and all eigenvalues of given matrix
4. Write a system of linear equations for given matrix

Question of 3 Marks

1. Let W=span {x1,x2}, where , construct an orthogonal basis {v1,v2}for W.
2. Find the characteristics polynomial and egenvalues of matrix A=
3. Sow that coefficient matrix of the following linear system is strictly diagonal dominant

Question of 5 Marks

1. Find an upper triangular matrix R such that A=QR
2. Define T: by T(x)=A(x), find a basis B for with the property that is diagonalizable A= QR
3. Let A be a 2*2 matrix with egenvalues 4 and 2, with corresponding eigenvectors




4. Let x(t) be the position of a particle at time t, solve the initial value problem
5. Let L be a linear transformation from to define by L , show that ‘L’ is inventible and also find it’s inverse?