Question

Precisava de ajuda nessas duas questões sobre matrizes

Answer 1

47)

$det \: D = { \sin}^{2} \frac{\pi}{5} + { \cos }^{2} \frac{\pi}{5} = 1$

48)

A= [a₁₁ a₁₂ a₁₃] =[0 1 4]

[a₂₁ a₂₂ a₂₃] [1 0 1]

[a₃₁ a₃₂ a₃₃] [4 1 0]

a₁₁=(1–1)²=0²=0

a₁₂=(1–2)²=(–1)²=1

a₁₃=(1–3)²=(–2)²=4

a₂₁=(2–1)²=(1)²=1

a₂₂=(2–2)²=0²=0

a₂₃=(2–3)²=(–1)²=1

a₃₁=(3–1)²=(2)²=4

a₃₂=(3–2)²=(1)²=1

a₃₃=(3–3)²=0²=0

Det A= –1(–4)+4(1)=4+4=8

${A}^{T} = [0 \: 1 \: 4 ] \\ \: \: \: \: \: \: \: \: \: \: \: \: [1 \: 0 \: 1 ] \\ \: \: \: \: \: \: \: \: \: \: \: \: [4 \: 1 \: 0 ]$

Daí

$det \: {A}^{T} = det A = 4 + 4 = 8$