find the determinant

Question

If a 4×4 matrix A with rows v1, v2, v3, and v4 has determinant detA=7,

row 1 [ v1]

row 2 [ 4v2 + 9v4 ]

row 3 [ v3 ]

row 4 [3v2 + 2v4 ]

what is the det of this matrix?

Answer 1

The determinant rules are

1) switching rows leads to neg of original determinant.

2) adding a multiple of a row to another row does not change the det.

3) multiplying a row by k, multiplies det by k

So, in this case new det = 4*2* old det.

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