The value of a determinant is a scalar quantity that represents a property of a square matrix. It can be calculated using methods like cofactor expansion or row operations. The value determines if a matrix is invertible and is used in solving linear equations using Cramer’s rule.
Chapter 4 of Class 12 Maths covers Determinants. It explains how to calculate determinants using methods like cofactor expansion and discusses their properties. The chapter also includes applications such as solving linear equations using Cramer’s rule and finding matrix inverses. These topics are crucial for students preparing for the CBSE Exam 2024-25.
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A square matrix A |A| = 5 find |AA T|
Theorem on Determinants for Matrix multiplication:
|AB| = |A||B|
AAᵀ For matrix multiplication. Then, using this theorem. |AA ᵀ |= |A|. |A|ᵀ|
AṀ A being a square Matrix
| AṀ ṀT|= |AT |
Hence, |Aᵀ| = |A|.
And we get;
|AA T |= | A||A | = | A|²
Since, the value of A = 5
|AAᵀ| = 5² = 25
Therefore, the correct value of |AAᵀ| is 25.
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