MATRICES
-----------
![Image for 1. Suppose A = [a1 a2 a3] is a 4x3 matrix, b is a vector in R^4, and x =[] is a solution of Ax = b. For ea](http://d2vlcm61l7u1fs.cloudfront.net/media%2F6c7%2F6c76058d-0d4f-43a5-ba5b-d79a40f81913%2Fphpo5ebTU.png)
-----------------
-----------
For details see post on
26-Feb-2015 at 6:00 am.
-------------![Image for 1. Suppose A = [a1 a2 a3] is a 4x3 matrix, b is a vector in R^4, and x =[] is a solution of Ax = b. For ea](http://d2vlcm61l7u1fs.cloudfront.net/media%2F6c7%2F6c76058d-0d4f-43a5-ba5b-d79a40f81913%2Fphpo5ebTU.png)
-----------------
| A= | [A1,A2,A3] | ||||||
| A1= | A2= | A3= | X= | B= | |||
| C | G | L | 2 | B1 | |||
| D | H | M | * | 1 | = | B2 | |
| E | J | N | 6 | B3 | |||
| F | K | P | B4 | ||||
| a)…TO CHECK VECTOR B IS IN SPAN OF A[A1,A2,A3] | |||||||
| A*X = B | |||||||
| THAT IS … | |||||||
| 2A1+A2+6A3=B | |||||||
| THIS CLEARLY IMPLIES THAT VECTOR B CAN BE WRITTEN | |||||||
| AS A LINEAR COMBINATION OF A1,A2,A3 | |||||||
| HENCE B IS IN THE SPAN OF A[A1,A2,A3] | |||||||
| PROVED | |||||||


0 Comments:
Post a Comment
<< Home