How can you find the inverse and determinant of matrices? How do you transpose a matrix? (H 2.01)

How are matrices used to solve systems of linear equations? (H 2.02)

What is a piecewise function? What do they look like? What are the key features? (H 2.03)



Answer :

Final answer:

Matrices: Inverse, Determinant, Transpose, and Solving Linear Equations are fundamental operations in mathematics using matrices.


Explanation:

Matrix Operations:

  • Finding Inverse and Determinant: The inverse of a matrix A, denoted as A-1, is a matrix that when multiplied by A gives the identity matrix. The determinant of a matrix determines if it is invertible or not.
  • Transposing a Matrix: Transposing a matrix involves switching its rows with its columns. For a matrix A, its transpose is denoted as AT.
  • Solving Linear Equations: Matrices can be used to represent systems of linear equations, where the coefficients are organized into matrices and solved using methods like Gaussian elimination or matrix inversion.

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