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NCERT Solutions Class 12 Maths Chapter 4 - Determinants

Q1: Write Minors and Cofactors of the elements of following determinants:
NCERT Solutions Class 12 Maths Chapter 4 - Determinants
Ans: (i) The given determinant is NCERT Solutions Class 12 Maths Chapter 4 - DeterminantsMinor of element aij is Mij.
NCERT Solutions Class 12 Maths Chapter 4 - Determinants
NCERT Solutions Class 12 Maths Chapter 4 - Determinants

Q2:
NCERT Solutions Class 12 Maths Chapter 4 - Determinants
Ans:
NCERT Solutions Class 12 Maths Chapter 4 - Determinants
NCERT Solutions Class 12 Maths Chapter 4 - Determinants
NCERT Solutions Class 12 Maths Chapter 4 - Determinants
NCERT Solutions Class 12 Maths Chapter 4 - Determinants
NCERT Solutions Class 12 Maths Chapter 4 - Determinants
NCERT Solutions Class 12 Maths Chapter 4 - Determinants

Q3: Using Cofactors of elements of second row, evaluate Δ =NCERT Solutions Class 12 Maths Chapter 4 - Determinants.
Ans: The given determinant is
NCERT Solutions Class 12 Maths Chapter 4 - Determinants .We have:
NCERT Solutions Class 12 Maths Chapter 4 - Determinants
NCERT Solutions Class 12 Maths Chapter 4 - Determinants
NCERT Solutions Class 12 Maths Chapter 4 - Determinants
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=  
NCERT Solutions Class 12 Maths Chapter 4 - Determinants
Ans: The given determinant is NCERT Solutions Class 12 Maths Chapter 4 - Determinants
.NCERT Solutions Class 12 Maths Chapter 4 - Determinants
We know that Δ is equal to the sum of the product of the elements of the second row
with their corresponding cofactors.
NCERT Solutions Class 12 Maths Chapter 4 - Determinants

Hence,

Q5: If ∆ =

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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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