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Answer to Question #23849 in Matrix | Tensor Analysis for habtewold assefa

Question #23849
1.Show that the set V of real valued functions defined on [0,1] with addition defined as (f+g)(x)=f(x)+g(x) and scalar multiplication(αf)(x) =αf(x)for α£R,is a vector space over R
2.Find the parametric equation and symmetric equations for the line though the points (5,3,1)&(2,1,1)
3.let V=R3 and
Determinate whether
W1={(a,b,c)}:c>0}.
W2={(a,b,c):a2+b2<=0.}
4.sho that S={(1,1,3),(0,-1,2),(1,0,1)}is a basis for R3
5.find a unit vector whose direction is opposite to the vector i-3j -5k
6.given (1 0 0,0 1/2 0 ,0 0 -1/3)A(1 1,1 2)=(1 0,0 1,0 0)find A
7.find the value of X A=[ 1 1 0,1 0 -1,1 2 x] is invertible .in that case give A-1

8.show that S={(1,1),(-1,2)}is a generator of R2
9.is (3,2,2)a linear combination of (a)(0,1,1),(2,0,0),(1,0,0)?(b)(1,0,0)(2,2,1)
10,let u and V be vectors with π/3the angle b/n them ,if//u//=2and //V//=3then find U.V and U.U
11.find the inverse of the matrix A=(-1 3 7 5,-1 2 -1 3,2 0 1 4,1 -1 -1 3) if possible
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