For which real numbers k does the set S = {<k,1,1>, <1,0,1>, <1,1,3k>} form a linearly dependent set in R3?
For which real numbers k does the set S = {<k,1,1>, <1,0,1>, <1,1,3k>} form a linearly dependent set i...
For which real values of x do the following vectors form a linearly dependent set in R3?v1= (x, -1/9, -1/9)v2= (-1/9, x, -1/9) v3= (-1/9, -1/9, x)
Determine whether the set S is linearly independent or linearly dependent. 2 -4 S={ 3 2 Note: you can only submit each part of this question once for marking. 2 -4 STEP 1: Determine if is a scalar multiple of 3 2 O scalar multiple O not a scalar multiple STEP 2: Determine if the set S is linearly dependent. O linearly independent linearly dependent
(a). Determine whether the set is linearly dependent or independent. Further, if it is linearly dependent, express one of the polynomials as a linear combination of others. (b). Determine whether the set can be considered as a basis of the vector space P2, which is the set of all polynomials of degree not more than 2 under addition and scalar multiplication. (1). B = {1 – 2,1 – 22, x – x2} (Hint: Similar to the matrix case in last...
*) . Determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them of the form C. Cz, and C as real numbers. If the vectors are linearly independent, enter INDEPENDENT.) *(). *--(). *»( (C1,C2,C)-
Determine whether the set Sis linearly independent or linearly dependent. S = {0, 0, 1, 0), (0, 1, 1, 0), (1, 1, 1, 0), (1, 1, 1, 1)} linearly independent linearly dependent
Q3. Determine whether the set of vectors in P2 is linearly dependent or linearly independent. S= {2 - x, 4x – x², 6-7x + x>). Q4. Show that the following set is a basis of R. --00:07)}
Explain why S is not a basis for M2,2 s-1 1 S is linearly dependent S does not span M2,2 S is linearly dependent and does not span M2,2 Explain why S is not a basis for M2,2 s-1 1 S is linearly dependent S does not span M2,2 S is linearly dependent and does not span M2,2
(a) In the vector space, V = {f : R → R}, prove that the set {x9,sin5x,cos2x} is linearly independent. (b) Is {(1,2,3),(−2,1,0),(1,0,1)} a basis for R3? Justify your answer.
Problenn 12: Decide whether the set S-le-,e,elr) is linearly independent or linearly dependent on R