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Understanding Identity and Inverse Matrices: Key Concepts in Linear Algebra

This resource explores the fundamental concepts of the identity matrix and the inverse matrix in linear algebra. The identity matrix, represented as Capital I, is a square matrix with ones on the principal diagonal and zeros elsewhere. It serves as the multiplicative identity for matrix multiplication. The inverse of a matrix A is denoted as A⁻¹, applicable only for square matrices with a non-zero determinant. Learn how to identify, calculate, and understand these matrices, along with their significance in real-number systems and matrix operations.

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Understanding Identity and Inverse Matrices: Key Concepts in Linear Algebra

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  1. Math 3 Warm Up 8/19/13 1. 2.

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  3. 2.

  4. Identity Matrix Aug. 19, 2013

  5. Identity Matrix • Capital I represents the identity matrix • A square matrix • The main (principal) diagonal (upper left to lower right) is all ones • All other elements are 0 • What is it in the real number system? • ?

  6. Identity Matrix I for a 3 x 3 matrix : What is I for a 2 x 2 matrix? For a 4 x 4 matrix?

  7. Inverse Matrix Aug. 19, 2013

  8. Inverse Matrix • The inverse of matrix A is denoted as . • You can only find the inverse of a square matrix • What is a square matrix? • The inverse matrix is the multiplicative inverse of the matrix • What is a multiplicative inverse? • No row can be a multiple of another row • Determinant ≠ 0 (If determinant = 0 then the matrix doesn’t have an inverse.)

  9. How do you find ? (switch & change)

  10. Find the inverse of matrix .

  11. Find the inverse of matrix .

  12. Now for Graphing Calculators!!!

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