Algebra -- Trig Evaluate the Determinant: | Research Paper

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Algebra -- Trig

Evaluate the determinant: | 3-9 |

Determinant of a square matrix can be solved by the following equation: A = ad -- bc, where a = 3, b = 9, c = 6, and d = 4. Therefore, A = (3)(4) -- (9)(6) = 12 -- 54 = -42

Solve the following system of equations using matrices:

y + 4z = 6, 2x + z = 1, x + 5y + z = -9

[ 1-5-1 | -9 ]

Row 2: R2 -- 2R1 = [ 2-0-1 | 1 ] -- 2[ 1 -1-4 | 6

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] = [ 0-2 -7 | -11 ]

Row 3: R3 -- R1 = [ 1-5-1 | -9 ] -- [ 1 -1-4 | ] = [ 0- -3 | -15 ]

New matrix:

[ 0-2 -7 | -11 ]

[ 0- -3 | -15 ]

Row 2: R2/2 = [ 0-1 -7/2 | -11/2 ]

Row 3: R3 -- 3R2 = [ 0- -3 | -15 ] -- 3[ 0-2 -7 | -11 ] = [ 0-0-18 | 18 ]

Converting back to system of equations:

x -- y + 4z =

y -- 7/2z = -11/2.....

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