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Math 225 final review uiuc
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  • Math 225 fnal rview uiuc
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  • Chamberlian School Of Nursing

Span( V1,...,VP) set of all linear combinations Basis of a vector subspace Let H be a subspace of a vector space V. An indexed set B=(v1,...vp) in V is a basis for H if: (i) B is a linearly independent set (ii) the subspace spanned by B coincides with H, that is, H=span(v1,...,vp

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  • February 19, 2024
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  • 2023/2024
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  • math 225 final review uiuc

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  • Chamberlian School Of Nursing
  • Math 225 fnal rview uiuc
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Math 225 final review uiuc

Span( V1,...,VP)

set of all linear combinations




Basis of a vector subspace

Let H be a subspace of a vector space V. An indexed set B=(v1,...vp) in V is a basis for H if:

(i) B is a linearly independent set

(ii) the subspace spanned by B coincides with H,

that is, H=span(v1,...,vp)



Linearly Independent

c1V1+c2V2+...cpVp=0 has only trivial solution (c1,....,cp=0)




Linearly dependent

c1V1+c2V2+...cpVp=0 such that c1,...cp not all to 0




Definition of a Transpose of a matrix

An nxm matrix A^T whose columns are the corresponding rows of the mxn matrix A.




(A^T)^T=

A

, (A+B)^T

A^T+B^T




(rA)^T

rA^T




(AB)^T

B^TA^T




A^(-1)

1/detA (adjA)




det(A)

ad-bc (cross product)




adjA

(cij)^T




solve Ax=b (using A^(-1))

x=A^(-1)b




(A^-1)^-1

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