cramer’s rule
DESCRIPTION
Cramer’s Rule. Applying Determinants to solve Systems of Equations 2x2 & 3x3. 2x2 Determinants. Det A = ad – cb. Cramer’s Rule for 2x2. Part 1 1.Extract Coefficients 2.Calculate Determinant of Original Matrix. Cramer’s Rule for 2x2. Part 2 (Solving for x ) - PowerPoint PPT PresentationTRANSCRIPT
Cramer’s RuleApplying Determinants to
solve Systems of Equations
2x2 & 3x3
2x2 Determinants
Det A = ad – cb
dc
baA det
Cramer’s Rule for 2x2
Part 11. Extract Coefficients
2. Calculate Determinant of Original Matrix
92
1232
yx
yx
21
32
1343122
Part 2 (Solving for x)3. Replace the 1st column of the
coefficient matrix with the constant matrix.
4. Calculate the determinant of new matrix & divide by original determinant.
Cramer’s Rule for 2x2
29
312
21
32
39212 511
51 x
Part 3 (Solving for y)5. Replace the 2nd column of the
coefficient matrix with the constant matrix.
6. Calculate the determinant of new matrix & divide by original determinant.
Cramer’s Rule for 2x2
91
122
21
32
12192 301
30 y
Part 47. To check x and y, substitute 51 in
for x and 30 in for y.
Cramer’s Rule for 2x2
930251
12303512
Part 1: 2 0
1 12
Ex #4 Solve
Part 2: 16 0
6 116 0 16
16
28
x
Part 3: =y
y
2 16
1 64
4
22
3x3 Determinants
cdhbfgaei
Downward
:
hg
ed
ba
ihg
fed
cba
Adet
idbhfag
Upward
ec
:
Cramer’s Rule for 3x3
Part 11. Extract coefficients.
2. Calculate Original Determinant (OD) of Matrix
2 1 2
2 0 1
1 3 4
2 1
2 0
1 3
Cramer’s Rule for 3x3Part 2 (Solving for x)
3. Replace the 1st column of the coefficient matrix with the constant matrix.
4. Calculate the determinant of new matrix & divide by original determinant (15).
7 1 2
5 0 1
10 3 4
7 1
5 0
10 3
40 1 39 x 39
152 6.
Cramer’s Rule for 3x3Part 3 (Solving for y)
5. Replace the 2nd column of the coefficient matrix with the constant matrix.
6. Calculate the determinant of new matrix & divide by original determinant (15).
2 7 2
2 5 1
1 10 4
2 7
2 5
1 10
y 33
152 2.
Cramer’s Rule for 3x3Part 4 (Solving for z)
7. Replace the 3rd column of the coefficient matrix with the constant matrix.
8. Calculate the determinant of new matrix & divide by original determinant (15).
2 1 7
2 0 5
1 3 10
2 1
2 0
1 3
z 3
150 2.
Part 59. To check x and y, substitute 2.6
in for x, 2.2 in for y, and 0.2 in for z.
Cramer’s Rule for 3x3