If my answers are right don’t solve them. 1) Show that the
If my answers are right don’t solve them. 1) Show that the mapping… If my answers are right don’t solve them. 1) Show that the mapping of F is linear. I did this by : * replacing (x1,x2,x3) with F(y1,y2,y3) and F(z1,z2,z3) and calculate the result then I did the same but for F(y1+z1,y2+z2,y3+z3), then I showed that F(y1,y2,y3) + F(z1,z2,z3) = F(y1+z1,y2+z2,y3+z3).* and I showed that if we have a constant $c in Z$ then F(c*x1,c*x2,c*x3) = c*F(x1,x2,x3) 2) Give the basis of Im(F). (Im is the image), here I built a matrix (1,0,1)(2,-1,0)(1,0,2)(-1,0,-1)then I transpose it to have:1,2,1,-10,-1,0,01,0,2,-1and I made it to row echleon form I got the basis, is this correct? 3) find the Rank and Nullity of Fshow transpose the matrix here to get the rank ?im not sure how to find them Math Linear Algebra MATH 347
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