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Inverse of a Matrix and Its Applications — Revision Notes

Telangana Open School (TOSS) · Class 12 · Mathematics

Inverse of a Matrix and Its Applications revision notes for Telangana Open School (TOSS) Class 12 Mathematics: 4 topics in quick points.

55 questions25 flashcards9 formulas & key relations5 concepts

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Key Topics to Revise

1

Singular and Non-Singular Matrices

  • A square matrix is singular if its determinant is zero.
  • A matrix is non-singular if its determinant is non-zero.
  • Only non-singular matrices have inverses.
2

Minors and Cofactors

  • Minor of an element is the determinant of the submatrix formed by deleting its row and column.
  • Cofactor includes a sign based on the position: C_ij = (-1)^(i+j) × M_ij.
  • Cofactors are used to form the adjoint matrix.
3

Adjoint of a Matrix

  • Adjoint is the transpose of the cofactor matrix.
  • For a 2×2 matrix, swap diagonal elements and change signs of off-diagonals.
  • Adjoint is used in the formula for inverse: A⁻¹ = (1/|A|) Adj A.
4

Inverse of a Matrix

  • The inverse A⁻¹ satisfies AA⁻¹ = A⁻¹A = I.
  • A⁻¹ exists only if |A| ≠ 0.
  • Formula: A⁻¹ = (1/|A|) Adj A.

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Full Notes

Key Concepts

A square matrix is singular ifThe minor of an elementThe adjoint of a matrixThe inverse of a matrixA system of linear equations can

Frequently Asked Questions

What are the important topics in Inverse of a Matrix and Its Applications for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Inverse of a Matrix and Its Applications include Singular and Non-Singular Matrices, Minors and Cofactors, Adjoint of a Matrix, Inverse of a Matrix. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Inverse of a Matrix and Its Applications for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 55 practice questions on Inverse of a Matrix and Its Applications. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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