MATH115-Week12.pdf - Math 115 Find a Week basis 2 for subspaces Lecture Example 47 if Determine We need p c if pi x capzlx 2 Fix c Xo X 2x x 2cg c terms

# MATH115-Week12.pdf - Math 115 Find a Week basis 2 for...

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Math 115 - Week 2 Findabasisforsubspaces
Lecture 47 Example : Determine if p { x 2x ' , x x ' , 2 x ' } is linearly independent TY Fix , Tax ) We need to determine if we obtain the t rival solution to c , pi ( x ) capzlx ) Csps ( x ) , a , a. GEIR e , X XZ Grouping the Xo , X , X ' terms , we obtain c , ( x 2x ' ) a C x x ) ( 2 x ' ) ( c , 2cg ) ( c , Cz ) x ( 2C , Cz Cs ) x x ' Putting this into a matrix and row reducing gives 2 2 2 Rz Ri Rst R2 2 2 Rs -212 , 2 5 7 each column has the coefficient of each polynomial ( a box CX ) becomes § Since the matrix is upper triangular , so it can be reduced to s giving the t rival solution , i. e. , p is linearly independent man We will go through some examples showing how to find a basis for a subspace of a vector space Example : find a basis for the subspace defined by a b S { ca Cb ER ' a , b. CER } .
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Span { , , } Span { , } and so C is a basis