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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 ] = [ 0-2 -7 | -11 ]
Row 3: R3 -- R1 = [ 1-5-1 | -9 ] -- [ 1 -1-4 | 6 ] = [ 0-6 -3 | -15 ]
New matrix:
[ 0-2 -7 | -11 ]
[ 0-6 -3 | -15 ]
Row 2: R2/2 = [ 0-1 -7/2 | -11/2 ]
Row 3: R3 -- 3R2 = [ 0-6 -3 | -15 ] -- 3[ 0-2 -7 | -11 ] = [ 0-0-18 | 18 ]
Converting back to system of equations:
x -- y + 4z = 6
y...
Perform the matrix row operation(s) and write the new matrix [ 2, -4, 1| 4]
[ -5, 0, 1| -3]
[ -1, 5, -2| -1]
-3R1 + R2
-3R1 = -3[ 2 -4-1 | 4 ] = [ -6-12 -3 | -12 ]
-3R1 + R2 = [ -6-12 -3 | -12 ] + [ -5-0-1 | -3] = [ -11-12 -2 | -15 ]
Answer: [ -11-12 -2 | -15 ]
5. Use Cramer's rule to solve the given…
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