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NCERT Solutions Class 12 Maths Chapter 4 - Determinants
Q1: Write Minors and Cofactors of the elements of following determinants:
Ans: (i) The given determinant is 
Minor of element aij is Mij.
Q2:
Ans:
Q3: Using Cofactors of elements of second row, evaluate Δ =
.
Ans: The given determinant is
.We have:
We know that ∆ is equal to the sum of the product of the elements of the second row with their corresponding cofactors.
∆ = a21A21 + a22A22 + a23A23 = 2(7) + 0(7) + 1(−7) = 14 − 7 = 7.
Q4: Using Cofactors of elements of third column, evaluate Δ= 
Ans: The given determinant is 
.
We know that Δ is equal to the sum of the product of the elements of the second row
with their corresponding cofactors.
Hence,
Q5: If ∆ =
The document NCERT Solutions Class 12 Maths Chapter 4 - Determinants is a part of the JEE Course Mathematics (Maths) Class 12.
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FAQs on NCERT Solutions Class 12 Maths Chapter 4 - Determinants
| 1. What is a determinant in mathematics? |  |
Ans. In mathematics, a determinant is a scalar value that can be calculated from the elements of a square matrix. It provides important information about the matrix, such as whether the matrix is invertible or singular.
| 2. How is the determinant of a 2x2 matrix calculated? | |
Ans. For a 2x2 matrix [[a, b], [c, d]], the determinant is calculated as ad - bc.
| 3. What does it mean if the determinant of a matrix is zero? | |
Ans. If the determinant of a matrix is zero, it means that the matrix is singular and does not have an inverse. This implies that the matrix's columns or rows are linearly dependent.
| 4. How is the determinant of a 3x3 matrix calculated? | |
Ans. For a 3x3 matrix [[a, b, c], [d, e, f], [g, h, i]], the determinant can be calculated using the Rule of Sarrus or by expanding along a row or column.
| 5. Why are determinants important in linear algebra? | |
Ans. Determinants play a crucial role in linear algebra as they help determine whether a system of linear equations has a unique solution, no solution, or infinitely many solutions. They also provide information about the properties of matrices and are used in various mathematical applications.
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