1. Let X be the set of vectors in R3 which are orthogonal to both 2 and 1 Express X in two ways: first, by finding a mat

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1 Let X Be The Set Of Vectors In R3 Which Are Orthogonal To Both 2 And 1 Express X In Two Ways First By Finding A Mat 1 (30.72 KiB) Viewed 25 times

1. Let X be the set of vectors in R3 which are orthogonal to both 2 and 1 Express X in two ways: first, by finding a matrix A for which X = Null(Ā), then by finding a matrix B for which X = Col(B). There are many different possible choices for A and B, but there is only one possible value for the rank of each. Explain what the rank of A must equal, and what the rank of B must equal, and why. 2. Write the following system of equations as a matrix equation Ax = b, find the general solution, and describe the solution geometrically. 21 +222 + 3x3 =15 21 +12 - 3x3 =12