The value of the determinant 43. | √(13)+√(3) √(5) √(5) √(15)+√(26) 5 √(10)

step 1 Problem 38 we want to find the value of the determinant square root of 13 plus square of 3 squar

The value of the determinant 43. | √(13)+√(3) √(5) ...

The value of the determinant 43. $\left|\begin{array}{ccc}\sqrt{13}+\sqrt{3} & \sqrt[2]{5} & \sqrt{5} \\ \sqrt{15}+\sqrt{26} & 5 & \sqrt{10} \\ 3+\sqrt{65} & \sqrt{15} & 5\end{array}\right|$ is (A) $-5 \sqrt{3}(5-\sqrt{6})$ (B) $-5 \sqrt{3}(5+\sqrt{6})$ (C) $-5 \sqrt{3}(\sqrt{6}-5)$ (D) None of these

The value of the determinant
43.
$\left|\begin{array}{ccc}\sqrt{13}+\sqrt{3} & \sqrt[2]{5} & \sqrt{5} \\ \sqrt{15}+\sqrt{26} & 5 & \sqrt{10} \\ 3+\sqrt{65} & \sqrt{15} & 5\end{array}\right|$ is
(A) $-5 \sqrt{3}(5-\sqrt{6})$
(B) $-5 \sqrt{3}(5+\sqrt{6})$
(C) $-5 \sqrt{3}(\sqrt{6}-5)$
(D) None of these

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Key Concepts

Simplification of Radical Expressions

When matrix entries involve irrational numbers like square roots, careful simplification of radical expressions is required. This includes combining like terms, rationalizing denominators, and accurately performing arithmetic operations with radicals to simplify the overall expression.

Cofactor Expansion

Cofactor expansion is a method used to compute determinants by expanding along a row or column. Each element of the selected row or column is multiplied by its corresponding cofactor, which is the determinant of the submatrix formed by deleting the element's row and column, with an appropriate sign based on its position.

Determinant

A determinant is a scalar value computed from a square matrix that provides important information about the matrix, such as whether it is invertible and the scaling factor for volumes under the associated linear transformation.

Matrix Determinant Computation

For a 3x3 matrix, the determinant can be calculated via methods such as the cofactor expansion or the rule of Sarrus. This involves breaking down the determinant into smaller determinants of 2x2 matrices and combining them appropriately to obtain the final value.

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