Prove that if matrix A and matrix B are similar n×n matrices, then they have
the same eigenvalues.
(1) Find the least squares solution of the following system Ax = b .
(2) Find the orthogonal projection of b onto the column space of A.
(1) Find the determinant of the matrix A by using cofactors method.
(2) Show the sum of all eigenvalues of A .
Solve the following initial value problem.
y´´+ 2ty´− 4y = 1, y(0) = y´(0) = 0
Find the inverse Laplace transform of the following function.
Show that if v(x, y) is a harmonic conjugate of u(x, y) , then their product uv is
also harmonic.
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