Let V = (a) Suppose a vector 1 3 2 = X1 X2 4683 X 3...

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Let V₁ = (a) Suppose a vector 1 3 2 = X1 X2 4683 X 3 X4 0 and V3 = D is orthogonal to all three vectors V₁, V2 and v3. Write down a system of linear equations satisfied by the components x1, x2, x3, x4. (b) Find a unit vector in R4 that is orthogonal to all three vectors V₁, V2, and v3. (c) Construct a 2 x 4 matrix whose nullspace is the span of {V₁, V2}. Let V₁ = (a) Suppose a vector 1 3 2 = X1 X2 4683 X 3 X4 0 and V3 = D is orthogonal to all three vectors V₁, V2 and v3. Write down a system of linear equations satisfied by the components x1, x2, x3, x4. (b) Find a unit vector in R4 that is orthogonal to all three vectors V₁, V2, and v3. (c) Construct a 2 x 4 matrix whose nullspace is the span of {V₁, V2}.

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Solution a Since V3 is orthogonal to all three vectors V V2 and V3 we have V V3 0 V2 V3 0 V3 V3 V32 ... View the full answer