SOLUTION: If a 4×4 matrix A with rows v1, v2, v3, and v4 has determinant detA=−8, then det [4v1 + 3v3] [ v2 ] [3v1 + 8v3] [ v4 ] = _?

Algebra ->  Matrices-and-determiminant -> SOLUTION: If a 4×4 matrix A with rows v1, v2, v3, and v4 has determinant detA=−8, then det [4v1 + 3v3] [ v2 ] [3v1 + 8v3] [ v4 ] = _?       Log On


   

Question 1159588: If a 4×4 matrix A with rows v1, v2, v3, and v4 has determinant detA=−8, then det
[4v1 + 3v3]
[ v2 ]
[3v1 + 8v3]
[ v4 ]
= _?
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.

It assumes that you know properties of determinant and can play and understand their music easily.


Step 1


    Adding  3v3  to the first row DOES NOT change the determinant.

    So, you can omit this addend from the first row.



Step 2


    Adding 3v1 to the third row  DOES NOT change the determinant.

    So, you can omit this addend from the third row.



Step 3


    So, you are left with THIS determinant

        [ 4v1 ]

        [ v2 ]

        [ 8v3 ]

        [ v4 ]


Step 4


    So, the value of the new determinant is  4*8 = 32 times the value of the original determinant.


ANSWER.  The value of the new determinant is  32*(-8) = - 256.

Solved.