The determinant Δ=| √13+√3 2 √5 √5 √15+√26 5 √10 3+√65 √15 5 | text equals

Question

The determinant Δ=| √13+√3 2 √5 √5 √15+√26 5 √10 3+√65 √15 5 | text equals  (A) 15 √2-25 √3 (B) 25 √3-15 √2 (C) 3 √5 (D) -15 √2+7 √3

Tardigrade Admin · Accepted Answer

Taking √5 common from C2 and C3, we get Δ=(√5)2|√13+√3 2 1 √15+√26 √5 √2 3+√65 √3 √5| Applying C1 arrow C1-√13 C3-√3 C2, we get Δ =(5)|-√3 2 1 0 √5 √2 0 √3 √5|=5(-√3)(5-√6) =5(√18)-25 √3=15 √2-25 √3

Q. The determinant $Δ = ∣ ∣ 13 + 3 15 + 26 3 + 65 255155105 ∣ ∣ equals$

$152 - 253$

$253 - 152$

$35$

$- 152 + 73$

Taking $5$ common from $C_{2}$ and $C_{3}$ , we get
$Δ = (5)^{2} ∣ ∣ 13 + 3 15 + 26 3 + 65 253125 ∣ ∣$
Applying $C_{1} \to C_{1} - 13 C_{3} - 3 C_{2}$ , we get
$Δ = (5) ∣ ∣ - 3 00 253125 ∣ ∣ = 5 (- 3) (5 - 6)$
$= 5 (18) - 253 = 152 - 253$

Q. The determinant Δ=∣∣​13​+3​15​+26​3+65​​25​515​​5​10​5​∣∣​ equals

152​−253​

253​−152​

35​

−152​+73​

Q. The determinant $Δ = ∣ ∣ 13 + 3 15 + 26 3 + 65 255155105 ∣ ∣ equals$

$152 - 253$

$253 - 152$

$35$

$- 152 + 73$