Find 3x3 matrix such that determinant(a)>0
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Here is the sol.=
Thematrix⎛⎝⎜147258369⎟(123456789)works just fine :the columns are in arithmetic progression, which means that the middle column is the arithmetic mean of the extremal columns, and thus they are not independent.for any 2×22×2 submatrix, the difference of the columns is a multiple of (11)(11), but none of the column is, so the columns must generate a space of dimension 22, hence they are linearly independent.
hpe it helps
Thematrix⎛⎝⎜147258369⎟(123456789)works just fine :the columns are in arithmetic progression, which means that the middle column is the arithmetic mean of the extremal columns, and thus they are not independent.for any 2×22×2 submatrix, the difference of the columns is a multiple of (11)(11), but none of the column is, so the columns must generate a space of dimension 22, hence they are linearly independent.
hpe it helps
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