1. Is there a solution of the following system of linear equations, which satisfies that the value of variable x1+2x2+2x3+x4=10 x2 is exactly the double of that of 4x1+5x2+3x3+11x4=22 variable x3 ? 2. Give a system of linear equations whose solution set is exactly the subspace VR3 generated by vectors (1,1,2),(1,4,4), (3,3,2). 3. Let b1=(1,3,2),b2=(2,1,1) and B={b1,b2} be a basis of subspace VR3. Determine the coordinates [v]B of vector v=(1,7,8)V with respect to basis B. 4. For what value(s) of parameter p will the value of the determinant 12pp2000p032p03p be 42? 5. Let u=u1u2u3u4R4 and define f(u)=u2u3u4u1 furthermore let g(u)=u2u1u4u3. Is the function F(u)=g(f(u)) a linear mapping? If yes, then determine the matrix [F] of the linear mapping. Let A=203213122 and C=2004302427. Is there a matrix B R33, such that AB=C? If there exists, then calculate B