Then H and K are subspaces of . In fact, H and K are planes in through the origin, and they intersect in a line through 0. Find a nonzero vector w that generates that line. [Hint: w can be written as To build w, solve the equation

Solution 40 EStep 1 of 4Consider the vectors Suppose that the subspaces and intersect in a line through 0.The objective is to find a nonzero vector w that generates the line.Since and intersect in a line, so w is in both H and K.Therefore, w can be expressed as a linear combination of and also as a linear combination of .Thus, write the vector w as .Therefore, the following equation is obtained: