How Does Row Reduction Show that det(H) = 0 for Matrix H = Q - nI?

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The discussion focuses on proving that the determinant of the matrix H, defined as H = Q - nI, equals zero. Here, Q is an n x n matrix where each entry is 1, and I is the n x n identity matrix. The key to the proof lies in row reducing the matrix H, which reveals that all columns sum to zero, leading to a linearly dependent set of rows. Consequently, this confirms that det(H) = 0.

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j3n
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PLEASE HELP! a matrix proof..

Hey!

I really need help with this question if possible.

Let Q be an n x n matrix with each entry = 1
Let I be the n x n identity matrix
let H = Q-n*I
show that det(H) = 0

(hint: think of row reducing H)

Thanks a lot,
j3n
 
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The hint pretty much tells you what to do. This might help: What is the sum of each column?
 

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