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does not define a valid inner product on
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Differential Equations and Linear Algebra (4th Edition)
- Express (AB)(AB) in terms of unions and intersections that involve A,A,B,andBarrow_forwardRather than use the standard definitions of addition and scalar multiplication in R3, let these two operations be defined as shown below. (a) (x1,y1,z1)+(x2,y2,z2)=(x1+x2,y1+y2,z1+z2) c(x,y,z)=(cx,cy,0) (b) (x1,y1,z1)+(x2,y2,z2)=(0,0,0) c(x,y,z)=(cx,cy,cz) (c) (x1,y1,z1)+(x2,y2,z2)=(x1+x2+1,y1+y2+1,z1+z2+1) c(x,y,z)=(cx,cy,cz) (d) (x1,y1,z1)+(x2,y2,z2)=(x1+x2+1,y1+y2+1,z1+z2+1) c(x,y,z)=(cx+c1,cy+c1,cz+c1) With each of these new definitions, is R3 a vector space? Justify your answers.arrow_forwardConsider the matrices below. X=[1201],Y=[1032],Z=[3412],W=[3241] Find scalars a,b, and c such that W=aX+bY+cZ. Show that there do not exist scalars a and b such that Z=aX+bY. Show that if aX+bY+cZ=0, then a=b=c=0.arrow_forward
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