# Find A a 3x3 real symmetric matrix [closed]

Find A a 3x3 real symmetric matrix such that the linear map A: R3 to R3 with x to Ax satisfies null(A) = {a(1,1,1) : a in R}

If anyone has a slow detailed explanation, I'd appreciate it!

https://i.stack.imgur.com/doSKG.png

## closed as off-topic by Adrian Keister, RRL, Andrew, Shaun, sazFeb 5 at 21:17

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• Can you at least construct any matrix that has the correct null space? – amd Feb 5 at 1:45
The matrix $$B=\pmatrix{1&-1&0\\0&1&-1\\}$$ has null-space $$\Bbb R\pmatrix{1\\1\\1}.$$ The matrix $$A=B^tB$$ is symmetric, and has the same null-space.