2. Consider the plane through the origin that contains the two vectors = (1,0,2,2,0) and b...

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2. Consider the plane through the origin that contains the two vectors = (1,0,2,2,0) and b = (0,0,0,1,3) in R5. Suppose we want to find all vectors in R5 that are orthogonal to this plane. We can do this by solving Ax = 0 where A is the 2 5 matrix that has rows (1,0,2,2,0) and (0,0,0,1,3). (Recall that every homogeneous system is solving for the vectors orthogonal to the rows of A.) a. Find the general solution to this system. Write your answer in vector form. (That is, x=1+1+133, where 11, 12, 13 are your free variables.) b. Use the dot product to check that each of the vectors (v1, v2, v3) that make up your general solution are perpendicular to the original two vectors a and b in the plane. 2. Consider the plane through the origin that contains the two vectors = (1,0,2,2,0) and b = (0,0,0,1,3) in R5. Suppose we want to find all vectors in R5 that are orthogonal to this plane. We can do this by solving Ax = 0 where A is the 2 5 matrix that has rows (1,0,2,2,0) and (0,0,0,1,3). (Recall that every homogeneous system is solving for the vectors orthogonal to the rows of A.) a. Find the general solution to this system. Write your answer in vector form. (That is, x=1+1+133, where 11, 12, 13 are your free variables.) b. Use the dot product to check that each of the vectors (v1, v2, v3) that make up your general solution are perpendicular to the original two vectors a and b in the plane.