vector Q/Consider the real vector space R². For every X= (X/X2) ER². Let 11x11 = \xil+\x\. Show that 1.11 define a hormon R².
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- 28. Is C a real vector space? Explain.Describe the conditions that are required for vector space.Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is linearly independent. If yes, show work, if no state a linear combination among the vectors of the list that adds up to a vector in the list. I am having trouble grasping the concept so if anyone can explain this problem I'd appreciate it.
- Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is {v1,v2,v3} linearly independent? Write all zeroes if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of v1, v2, and v3. a). Is {v1,v2} linearly independent? Write all zeroes if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of v1 and v2. c). Write the dimension of span {v1,v2,v3}Thank you!Is the set of rational numbers with the usual definitions and scalar multiplication a vector space? Please show justification for answer and explain steps.
- If (x1,y1) + (x2,y2) = (x1x2,y1y2) and c(x1,y1)= (cx1,cy1) are vector spaces, verify if both are a vector space property and identify the properties that it will fail. (Use the 8 theorems). Assuming the +x-axis is horizontal to the right for the vectors in the following figure, find the following scalar products: (a) →A · →C ; (b) →A · →F; (c) →D · →C ; (d) →A · (→F + 2 →C); (e) ^i · →B; (f) ^j · →B; (e) (3 ^i − ^j) · →B, and (h) B^ · B→.
