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]]>Let A be a 3×3 matrix with real entries. Prove that if A is not similar over

R to a triangular matrix then A is similar over C to a diagonal matrix.

2x+3y = 1, 3x +2y = - 4 ? ]]>

Finite difference. A finite difference is a mathematical expression of the form f (x + b) − f (x + a). … The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.

]]>A nxn nonhomogeneous system of linear equations has a unique non-trivial solution if and only if its determinant is non-zero. If this determinant is zero, then the system has either no nontrivial solutions or an infinite number of solutions.

]]>A=⎡⎣⎢⎢11/41/21/41/31/41/21/41/5⎤⎦⎥⎥

the value of ‘theta θ’ can be found as

]]>2x+3y = 1, 3x +2y = - 4 ? ]]>

|a12|

be numerically the largest off-diagonal element of A, then we can construct orthogonal matrix S1 by Jacobi’s method as ]]>

9

]]>2x+z=4

x-y+z=-3

-y+z=-5 ]]>

**a) (1, 0.75)**

b) (0.25,1)

c) (0,0)

d) (1,0.65)

Eigenvectors of a matrix corresponding to distinct eigenvalues are linearly independent. . If λ is an eigenvalue of multiplicity k of an n × n matrix A, then the number of … power method converges to the smallest eigenvalue in absolute value of A. … v2, …, vn, and that λ1 is a simple eigenvalue with the largest magnitude, i.e.,.

]]>2x+y−3z=5

x+3y+2z=7

x+2y+z=3

can be rewritten as

]]>same

different

Two similar matrices have the **same** characteristic polynomial. The converse however is not true in general: two matrices with the same characteristic polynomial need not be similar.

**Iterative method**

Direct method