Numerical elements MCQ Quiz in తెలుగు - Objective Question with Answer for Numerical elements - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

Concept:

Properties of Determinant of a Matrix:

• If each entry in any row or column of a determinant is 0, then the value of the determinant is zero.
• For any square matrix say A, |A| = |AT|.
• If we interchange any two rows (columns) of a matrix, the determinant is multiplied by -1.
• If any two rows (columns) of a matrix are same then the value of the determinant is zero.

Calculation:

Apply C2 → 5C2 + C₁, we get

= 

As we can see that the second and the third column of the given matrix are equal. 

We know that, if any two rows (columns) of a matrix are same then the value of the determinant is zero.

∴  = 0

For 3X3 matrix,

Calculation

|p| = 2α - 6 = (det A)² = 16

⇒ α = 11

Hence option 2 is correct

Concept:

The co-factor of A_ij = (– 1)^i+jM_ij, where Mij is the minor obtained by removing the i^th row and j^th column.

Calculation:

Given, A =  and B = 

Now, equating co-factor fo A₂₁  = (2α² – 3α) = α

⇒ α = 2, 0

⇒ α = 2 [∵ α ≠ 0] 

Now, 2α² – αβ = 3α 

⇒ 8 – 2β = 6

⇒ β = 1

∴ |AB| = |A cof (A)| = |A|³ 

∴ |A| =  = 6 - 2(9) + 3(6) = 6

⇒ |A|3 = 63 = 216

∴ The value of det(AB) is equal to 216.

The correct answer is Option 4.

Concept:

Determinants:

• A linear combination of the rows/columns does not affect the value of the determinant.
• If two rows/columns of a given matrix are interchanged, then the value of the determinant gets multiplied by - 1.
• If a row/column of a given matrix is multiplied by a scalar k, then the value of the determinant is also multiplied by k.

Calculation:

Let D = .

Dividing R₁ by scalar 5² and R₂ by 5³, we get:

⇒ D = 

Using R₁ → R₁ - R₂, we get:

⇒ D = 

Expanding along R₁, we get:

⇒ D = 0.