Inverse matrix
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This document discusses inverse matrices. An inverse matrix A-1 undoes the transformation of the original matrix A such that multiplying A by A-1 or A-1 by A results in the identity matrix. The identity matrix is a square matrix with 1s on the main diagonal and 0s elsewhere. It leaves a matrix unchanged when multiplied. The determinant of a square matrix transforms it into a scalar value and is used to calculate the inverse. Sample problems demonstrate calculating the inverse of a 2x2 matrix.
Inverse matrix
- 1. INVERSE MATRIX(2x2)Cariaga, Melody KayeDelgado, Diana MarieFeliciano, Aila Marie
- 2. What is an Inverse Matrix?The inverse of a nonsingular matrix A is the matrix A-1 where A · A-1 = A-1 · A = I, theidentity matrix.
- 3. TERMS
- 4. Identity MatrixThe matrix I is called an identity matrix because IA = A and AI = A for all matrices A. This is similar to the number 1, which is called the multiplicative identity, because 1 a = a and a 1 = a for all real numbers a.Identity Matrix“unit matrix”
- 5. A square matrix which has a 1 for each element on the main diagonal and 0 for all other elements.
- 8. Determinantan algebraic expression that transforms a square matrix M into a scalar.
- 14. Solving the Inverse of a 2x2 Matrix
- 15. Sample Problem No. 1
- 16. Sample Problem No. 1
- 17. Sample Problem No. 1
- 18. Sample Problem No. 1
- 19. Sample Problem No. 1c
- 20. Sample Problem No. 1
- 21. Sample Problem No. 1
- 22. Sample Problem No. 1
- 23. Sample Problem No. 1
- 24. Sample Problem No. 1
- 25. Sample Problem No. 1
- 26. Proving:
- 27. Sample Problem No. 2
- 28. Sample Problem No. 2
- 29. Sample Problem No. 2
- 30. Sample Problem No. 2
- 31. Sample Problem No. 2
- 32. Sample Problem No. 2
- 33. Sample Problem No. 2
- 35. Proving: