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Let x ? R3 be nonzero and let A be the matrix whose columns are x,...

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Basic Math

Let x ? R3 be nonzero and letA be the matrix whose columns are x, 2x,3x in this order. Show that x is an eigenvector of A andfind a basis for the null space of A.

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Let x abcT where abc R and none of abc equals 0 so that x is not a zero vector Then A a 2a 3a b 2b 3b c 2c 3c The eigenvalues of A are solutions to the equation detAI3 0 or 3a22b23c2 0 or 2a2b3c 0    See Answer
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