Theorem 2 on Adjoint of Matrix

TL;DR

The adjoint of a matrix can be expressed as the determinant of the matrix times its inverse, and this relationship holds true even when inverted.

Transcript

hello in this session we'll see theorem 2 on adjoint of matrix so it says if a is a non-singular matrix of order n let's say then as we have already seen in the previous theorem that a times of adjoin a or is equal to determinant of a times of the identity matrix of order n and the other one also so from here what we can do is what if we multiply a... Read More

Key Insights

• 🚱 Theorem 2 provides a relationship between the adjoint, determinant, and inverse of a non-singular matrix.
• ❓ The formula for the adjoint of a matrix involves the determinant and inverse of the matrix.
• 🟰 The adjoint of a matrix and the adjoint of its inverse are equal.

Questions & Answers

Q: What is Theorem 2 on the adjoint of a matrix?

Theorem 2 states that if matrix A is non-singular, the adjoint of A is equal to the determinant of A times the inverse of A.

Q: How is the formula for the adjoint of A derived?

The formula is derived by multiplying both sides of the equation by the inverse of A and simplifying the result.

Q: What is the relationship between the adjoint of A and the adjoint of the inverse of A?

Both the adjoint of A and the adjoint of the inverse of A are equal, as shown by Theorem 2.

Q: How can the formula for the adjoint of A be expressed?

The formula can be expressed as 1 divided by the determinant of A times the matrix A.

Summary & Key Takeaways

• Theorem 2 states that if matrix A is non-singular, then the adjoint of A is equal to the determinant of A times the inverse of A.

• By multiplying both sides of the equation by the inverse of A, we can derive the formula for the adjoint of A.

• The result shows that the adjoint of A is the same as the adjoint of the inverse of A, and both are equal to 1 divided by the determinant of A times the matrix A.