《高等代數(shù)與解析幾何》英文習(xí)題

《高等代數(shù)與解析幾何》英文習(xí)題《高等代數(shù)與解析幾何》英文習(xí)題1.(Feb.28)Is 1 12 10 11 0

abasisforthelinearspaceof, , , 0 11 11 01 0all 22matrices?2.(Mar.1)uLet u

i2j

. Find vectors

and

that are bothvwuorthogonalto vwu3.(Mar.4)

andtoeachother.Let S,v1 2

,...,vn

}beabasisforalinearspaceV andletU beasubspaceof V.Isitnecessarilytruethatabasisfor U isasubsetofS?Why?4.(Mar.7)In(1)-(2)determinewhichofthegivenfunctionsareinnerproductson R3 where

u vu1

and v1 u2 v2 3 3(1)(,)2uv11v2 4uv;3 3(2)(,)uv13

uv2

uv.315.(Mar.8)InExercises(1)-(2)determinewhetherthegivensetofvectorsis1/4《高等代數(shù)與解析幾何》英文習(xí)題orthogonal,orthonormal,orneitherwithrespecttotheEuclideaninnerproduct.(1)(1,2),(0,3);(2)6.(Mar.11)Computetheareaofthetrianglewithvertices (0,2,7),,and(1,1,1).7.(Mar.14)Showthat||2||24(,).8.(Mar.15)InExercises(1)and(2)findanequationfortheplanethatpassesthroughthepointPandthatisparalleltotheplanewhosegeneralequationisgiven.(1)P;3x7y2z10.(2) P; 2x5y3z60.9.(Mar.18)LetT:R2R3 bealineartransformationsuchthat

0

1

2T

4, T

5.

T7;66

3

1yFindTy1/4《高等代數(shù)與解析幾何》英文習(xí)題Findamatrix A suchthatxTy

xA yA 10.(Mar.21)If,v1 2

,,vn

}spansalinearspace V,isitpossiblefor 2

,v,,v}3 ntospanV?Explainyouranswer.11.(Mar.22)InExercises(1)and(2)findparametricequationsforthelineofintersectionbetweentheplaneswhosegeneralequationsaregiven.(1)2x3y5z40; 2x5y6z20.(2)3x5y4z20; 4x7y2z10.12.(Mar.25)InExercises(1)-(2)namethesurfacedeterminedbythegivenequationandgiveitsequationinacoordinatesysteminwhichthesurfaceisinstandardposition.(1)4x2y22z28x4y10.(2) x23y2z26x18y16z48013.(Mar.28)InExercises(1)-(2)findthematrixrepresentationofthegiventransformationT:R3R[x]withrespecttotheorderedbases3Bfor R3 and B'x,x2}forR[x].3(1)T((a,b,c))ax2bxc.(2)T((a,b,c))(ab)xc.1/4《高等代數(shù)與解析幾何》英文習(xí)題14.(Mar.29)InExercises(1)-(2)findbasesforthekern