Homework SourseFind the dimension of the subspace H of R2 spanned by 2 5T
Find the dimension of the subspace H of R2 spanned by
[2 -5]T , [-4 10]T , [-3 6]T
Solution
The RREF of the matrix [ 2 -4 -3] is [ 1 -2 0 ] [-5 10 6] [ 0 0 1 ]
It is apparent that the vector ( -4,10)T = -2( 2,-5)T . Thus, only the vectors ( 2,-5)T and ( -3,6)T are linearly independent. Therefore, the dimension of H, the given subspace of R2 is 2.
![Find the dimension of the subspace H of R2 spanned by [2 -5]T , [-4 10]T , [-3 6]TSolutionThe RREF of the matrix [ 2 -4 -3] is [ 1 -2 0 ] [-5 10 6] [ 0 0 1 ] It](/WebImages/32/find-the-dimension-of-the-subspace-h-of-r2-spanned-by-2-5t-1091642-1761574897-0.webp "Find the dimension of the subspace H of R2 spanned by [2 -5]T , [-4 10]T , [-3 6]TSolutionThe RREF of the matrix [ 2 -4 -3] is [ 1 -2 0 ] [-5 10 6] [ 0 0 1 ] It")
