For questions 35 below recall that if Wi W2 are subspaces of

For questions 3-5 below, recall that if Wi, W2 are subspaces of a vector space V, we say that V is the direct sum of 111 and 112, written V = W, W2, if every v e l\' can be written uniquely as v = wi + w2 where w, E W, and w 2 E W2. Equivalently, V = Wew, if V-l + W2, and Win W2 = {0). cf. Textbook, Section 13: # 9

Solution

W₁ = {(x,0): x is real number}

W₂ = {(0,y): y is real number}

W₃ = {(x,x): x is real number}