1 / 16

The Inverse of a Matrix

The Inverse of a Matrix. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB. The inverse of a square matrix A is another matrix with the following properties:. Here I represents the identity matrix of the same size as A and A -1 .

saman
Télécharger la présentation

The Inverse of a Matrix

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Inverse of a Matrix Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  2. The inverse of a square matrix A is another matrix with the following properties: Here I represents the identity matrix of the same size as A and A-1. Note that A-1 must be a square matrix of the same size as A. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  3. The inverse of a square matrix A is another matrix with the following properties: Here I represents the identity matrix of the same size as A and A-1. Note that A-1 must be a square matrix of the same size as A. Here is a system of linear equations. To solve it, we can put it into matrix format and try to find the inverse of the coefficient matrix. Let’s see how that works. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  4. The inverse of a square matrix A is another matrix with the following properties: Here I represents the identity matrix of the same size as A and A-1. Note that A-1 must be a square matrix of the same size as A. Here is a system of linear equations. To solve it, we can put it into matrix format and try to find the inverse of the coefficient matrix. Let’s see how that works. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  5. To find the inverse, for an augmented matrix with the coefficient matrix on the left, and the corresponding identity matrix on the right. Next, row reduce until you have the identity on the left, and the inverse will be on the right. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  6. To find the inverse, for an augmented matrix with the coefficient matrix on the left, and the corresponding identity matrix on the right. Next, row reduce until you have the identity on the left, and the inverse will be on the right. Here is the method, applied to our example: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  7. To find the inverse, for an augmented matrix with the coefficient matrix on the left, and the corresponding identity matrix on the right. Next, row reduce until you have the identity on the left, and the inverse will be on the right. Here is the method, applied to our example: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  8. To find the inverse, for an augmented matrix with the coefficient matrix on the left, and the corresponding identity matrix on the right. Next, row reduce until you have the identity on the left, and the inverse will be on the right. Here is the method, applied to our example: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  9. To find the inverse, for an augmented matrix with the coefficient matrix on the left, and the corresponding identity matrix on the right. Next, row reduce until you have the identity on the left, and the inverse will be on the right. Here is the method, applied to our example: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  10. To find the inverse, for an augmented matrix with the coefficient matrix on the left, and the corresponding identity matrix on the right. Next, row reduce until you have the identity on the left, and the inverse will be on the right. Here is the method, applied to our example: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  11. To find the inverse, for an augmented matrix with the coefficient matrix on the left, and the corresponding identity matrix on the right. Next, row reduce until you have the identity on the left, and the inverse will be on the right. Here is the method, applied to our example: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  12. To find the inverse, for an augmented matrix with the coefficient matrix on the left, and the corresponding identity matrix on the right. Next, row reduce until you have the identity on the left, and the inverse will be on the right. Here is the method, applied to our example: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  13. To find the inverse, for an augmented matrix with the coefficient matrix on the left, and the corresponding identity matrix on the right. Next, row reduce until you have the identity on the left, and the inverse will be on the right. Here is the method, applied to our example: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  14. So now we have the inverse of our coefficient matrix. To solve the original system of equations, simply multiply through by this inverse matrix: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  15. So now we have the inverse of our coefficient matrix. To solve the original system of equations, simply multiply through by this inverse matrix: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

  16. So now we have the inverse of our coefficient matrix. To solve the original system of equations, simply multiply through by this inverse matrix: Thus we find a unique solution to the original system of equations. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

More Related