Please help me with these 2 questions. 5.3.6Matrix A is factored in the form PDPUse the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.20 -2-2 0- 130 00 01A=2 3 4120 3 01 40 03.10 0 2-10 -2Select the correct choice below and fill in the answer boxes to complete your choice.(Use a comma to separate vectors as needed.)O A. There is one distinct eigenvalue, =A basis for the corresponding eigenspace isВ.In ascending order, the two distinct eigenvalues are , =and 12 =Bases for the corresponding eigenspaces are { } and { }, respectively.O C. In ascending order, the three distinct eigenvalues are 1 =,12 =and A3 =Bases for the corresponding eigenspaces are { }. { }, and { }, respectively. Let B be the basis of P, consisting of the three Laguerre polynomials 1, 1-t, and 2-4t+t, and let p(t) = 4 - 4t + 2t. Find the coordinate vector of p relative to B.(p]g =

Name: Please help me with these 2 questions. 5.3.6Matrix A is factored in th
Uploaded: 2024-03-20T07:07:37.000Z
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Description: Please help me with these 2 questions. 5.3.6Matrix A is factored in the form PDPUse the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.20 -2-2 0- 130 00 01A=2 3 4120 3 01 40 03.10 0 2-10 -2Select the correct choi

Given: A=20-2234003=-20-1012100300030002001214-10-2 Since A is diagonalizable , P is an invertible matrix with columns that are linearly independent eigen vectors of A, and D is a diagonal matrix with entries on the diagonal that are eigenvalues of A. Thus the eigen values of A are: 2, 3, 3 and basis for the corresponding eigen spaces are -1,2,0 and -2,0,1,0,1,0 respectively. so, option b is true. In ascending order two eigen values are λ1=2 and λ2=3. Bases for corresponding eigenspaces are -1,2,0 and -2,0,1,0,1,0. 2 Let Pt=a1+b1-t+c2-4t+t24-4t+2t2=a1+b1-t+c2-4t+t2comparing both sides , we get4=a+b+2c-4=-b-4c2=c Therefore, a=4,b=-4 and c=2 ⇒PB=4, -4, 2