The value of the determinant Δ =| √13+√3 2√5 √5 √15+√26 5 √10 3+√65 √15 5 | is equal to

Question

The value of the determinant Δ =| √13+√3 2√5 √5 √15+√26 5 √10 3+√65 √15 5 | is equal to (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-√13C3-√3C2, 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 value of the determinant $Δ = ∣ ∣ 13 + 3 15 + 26 3 + 65 255155105 ∣ ∣$ is equal to

$152 - 253$

$253 - 152$

$35$

$- 152 + 73$

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 value of the determinant Δ=∣∣​13​+3​15​+26​3+65​​25​515​​5​10​5​∣∣​ is equal to

152​−253​

253​−152​

35​

−152​+73​

Q. The value of the determinant $Δ = ∣ ∣ 13 + 3 15 + 26 3 + 65 255155105 ∣ ∣$ is equal to

$152 - 253$

$253 - 152$

$35$

$- 152 + 73$