Let & be linear map from as Pacex into aspace and {X1, X2, – 1— x3 basis for x show that f a one-to-one isf {f(x1), f (xx); — F (Kn) } linearly independent. மம் let M be a Proper sub space of aspace X then M is ahyper space iff for any text&M X=. C) let X be a linear space and fe X1{0} Show that is bjective or not and why? ***********
Let & be linear map from as Pacex into aspace and {X1, X2, – 1— x3 basis for x show that f a one-to-one isf {f(x1), f (xx); — F (Kn) } linearly independent. மம் let M be a Proper sub space of aspace X then M is ahyper space iff for any text&M X=. C) let X be a linear space and fe X1{0} Show that is bjective or not and why? ***********
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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Transcribed Image Text:Let & be linear map from as Pacex into aspace
and {X1, X2, –
1—
x3 basis for x show that f
a one-to-one isf
{f(x1), f (xx); — F (Kn) } linearly independent.
மம்
let M be a Proper sub space of aspace X
then M is ahyper space iff for any text&M
X=<MV {+}>.
C) let X be a linear space and fe X1{0}
Show that is bjective or not and why?
***********
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