matrix A = 2 a-2b+c 2a+b+c 3 5 a+c 0 -2 7i know that a-2b+c=3 and son on ... but i cant seem to process the equation to get answers consistent for the equation.

find values for a, b, and c for which the matrix A is symmetric

matrix A = 2 a-2b+c 2a+b+c 3 5 a+c 0 -2 7i know that a-2b+c=3 and son on ... but i cant seem to process the equation to get answers consistent for the equation.

- stapel_eliz
**Posts:**1628**Joined:**Mon Dec 08, 2008 4:22 pm-
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For the matrix to be symmetric, it must be equal to its own transpose. In other words:

**the linear system** for the values of "a", "b", and "c".

Then plug these values back into the original expression of the matrix A.

[ 2 a-2b+c 2a+b+c ] [ 2 3 0 ] [ 3 5 a+c ] = [ a-2b+c 5 -2 ] [ 0 -2 7 ] [ 2a+b+c a+c 7 ]By equating entries (which is the definition of "matrix equality"), we get the following system:

1a - 2b + 1c = 3 2a + 1b + 1c = 0 1a + 0b + 1c = -2Solve

1a - 2b + 1c = 3 2a + 1b + 1c = 0 1a + 0b + 1c = -2 -R3 + R1 -> R1 - 2b = 5 2a + 1b + 1c = 0 1a + 0b + 1c = -2 1b = -2.5 2a + 1b + 1c = 0 1a + + 1c = -2 -R1 + R2 -> R2 1b = -2.5 2a + 0b + 1c = 2.5 1a + + 1c = -2 -(1/2)R2 + R3 -> R3 1b = -2.5 2a + 1c = 2.5 -(1/2)c = -3.25...and so forth.

Then plug these values back into the original expression of the matrix A.