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3. (10 points) Determine the multiplicity of each eigenvalue and a basis and dimension of each...


3. (10 points) Determine the multiplicity of each eigenvalue and a basis and dimension of each eigenspace and state whether t
3. (10 points) Determine the multiplicity of each eigenvalue and a basis and dimension of each eigenspace and state whether the matrix is diagonalizable or not. 1 6 -40 -7 0 0 -3 oni
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The answer for above problem is explained below.

Given that, 4 16 Az -4 o -7 o -3 For Eigen values, 30 | A-XI 1 = - 4-1 6 2 ) - 4 -7 a o -3- (4-1) (3x+2841(12 +41) +6 (0) = 0The eigen vector corresponding to x, =-3 is, 4 + 3 6 le :: 31.6 O 6 T IT. -4 3 3:13 - 7 o matrix Augmented ės, 7 6 > -4 3 ::: The - F eigen space, dim [E For d=2 Augmented matrix ės, 2 6 -4 -2 7 -5 R27 R2 + QR, 0 6 2 - = ) -5 B - R₂ + R₂ - ::: R, 1/-ام 3 N o o o rector is Eigen polu 10 -- dim (E2] = 1 <2 Calgebraic multiplicity of 1 = 2) .. Matrix diagonalizable A is

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