Explain why S is not a basis for R2.S = {(6, −5), (12, −10)}

Show that the polynomials P1 = 1+x + x² P2 = x + x² P3 = x2 form a basis for P2.

The set { (-2, 5) , (1, -1) } is a basis for R2 Select one: O True O False

find a basis for the range from r2 to r3 as defined by [3x1+4x2; x1-2x2; 4x1]

9. Let and B 3 = {[B]-[-2]} = B' ={[2¹].[6]} be two ordered bases for R². Find the change of basis matrix [I]B'.

[3 and v2 = 3 What values -2 Let S = {v1, V2} be a basis of R? where v1 = of ci and c2 satisfy the equation c1 Vị + C2V2 = ? – 10 O c1 = -9, c2 = -10 O c1 = -4, c2 = 1 O c1 = -4, c2 = 2 O c1 = -57, C2 = 2 %3D

The set of polynomials s a basis for IP2. Find the coordinate vector of elative to B. [p(t)]B = B = {3-4t,t−3+t²,− (7+7t+5t²)} p(t) = −3+(-2)t + 3t² in Cocalc). To solve this problem, you will at some point end up solving a system of linear equations; feel free to do that with a computer (e.g.,

Can you help me solve this problem? Thank you!