Sample Quiz

March 8, 2006
MTH 338: Linear Algebra

The determinant of (

7 -1
2 1
) is ______________________

The inverse of (

7 -1
2 1
) is _____________________

The reduced row echelon form of the matrix (

1 2 0 1
0 1 1 1
0 1 2 2
) is (
______ ______ ______ ______
______ ______ ______ ______
______ ______ ______ ______
).

The definition of the determinant is as follows:
    Det([a])  = a,
    and if A is an n×n matrix, then for any r between 1 and n (inclusive)
    Det(A) = a_ (r 1)A_ (r 1)+a_ (r 2)A_ (r 2)+ ... +a_ (r n)A_ (r n), where A_rj=(-1)^(r + j)Det(M_ (r j)) and M_ (r j) is the matrix obtained from A by deleting the r-th row and the j-th column.
    
Using this definition, prove that if two rows of A are identical, then Det(A)=0.

Solutions

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