SOLUTION: please help me with this:: is this statement true or false : matrix B & C are equivalent matrix B = ( matrix( 3, 4, 1, 3, -2, 2, -1, -2, -1, -1, -1, -5, 8, -3, ) ) and m

Algebra ->  College  -> Linear Algebra -> SOLUTION: please help me with this:: is this statement true or false : matrix B & C are equivalent matrix B = ( matrix( 3, 4, 1, 3, -2, 2, -1, -2, -1, -1, -1, -5, 8, -3, ) ) and m      Log On


   

Question 1031370: please help me with this::
is this statement true or false : matrix B & C are equivalent
matrix B =
(
matrix( 3, 4,
1, 3, -2, 2,
-1, -2, -1, -1,
-1, -5, 8, -3,
)
)
and matrix C=
(
matrix( 3,4,
1, 2, 1, 2,
1, 1, 4, 0,
1, -1, -4, 1,
)
)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Matrix B can be shown to be row-equivalent to %28matrix%283%2C4%2C1%2C0%2C-7%2C0%2C0%2C1%2C-3%2C1%2C0%2C0%2C0%2C1%29%29. A few more column operations would lead to equivalence to %28matrix%283%2C4%2C1%2C0%2C0%2C0%2C0%2C1%2C0%2C0%2C0%2C0%2C1%2C0%29%29.
By performing a sequence of row operations and then a sequence of column operations, matrix can also be shown to be equivalent to %28matrix%283%2C4%2C1%2C0%2C0%2C0%2C0%2C1%2C0%2C0%2C0%2C0%2C1%2C0%29%29.
Therefore matrices B and C are equivalent to the same row- and column-reduced matrix, and so they themselves are equivalent to each other.