PEM2036 Tutorial 1
 
Q1(i)
     (ii)
    (iii)


Q2(i)
(ii)

R2→R2–3R1   E21(-3)
R3→R3–R2   E32(-1)
R1→R1–R3   E13(-1)

E21(-3)E32(-1)E13(-1)
Q3


Q4

Q5 Non-singular matrix = inverse exists           det(B) ≠ 0   det(C) ≠ 0


 
 
Q6


Q7 (i)



Q7 (ii)


Q8 The characteristic equation: |λI-A|=0
       
              (λ–2)(λ–1) = 0
                   λ = 2, 1

       For λ = 2:  4(2)3 + 7(2)2 +3(2) – 1 = 65
       For λ = 1:  4(1)3 + 7(1)2 +3(1) – 1 = 13
Q9 (i)  Trace A = ∑λi = 2 + 3 + 9 = 14
 Det(A) = ∏λi = 2 x 3 x 9 = 54
 Eigenvalues for A-1 = 1/λi = 1/2, 1/3, 1/9
 
 

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