Use Cramer's Rule to solve for R1

Use Cramer's Rule to solve for R1 given that: 2R1 - 3R2 = 7 2R2 + 4R3 = 6 R1 - 5R3 = -3
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Using Cramer's Rule:

Create determinant from coefficients, we'll call D=

| 2 -3  0 |

| 0  2  4 |

| 1  0 -5 |

Evaluate: 2(-10)+3(-4)=-20-12=-32.

Create determinate D[R1] from coefficients and constants:

|  7 -3  0 |

|  6  2  4 |

| -3 0 -5 |

Evaluate, D[R1]=7(-10)+3(-18)=-124.

D[R2]:

| 2  7  0 |

| 0  6  4 |

| 1 -3 -5 |

D[R2]=2(-18)-7(-4)=-8.

D[R3]:

| 2 -3  7 |

| 0  2  6 |

| 1  0 -3 |

D[R3]=2(-6)+3(-6)+7(-2)=-44.

R1=D[R1]/D=-124/-32=31/8; (also R2=D[R2]/D=-8/-32=1/4; R3=D[R3]/D=-44/-32=11/8).

CHECK

2(31/8)-3/4=28/4=7. OK

2(1/4)+4(11/8)=6. OK

31/8-55/8=-24/8=-3. OK
by Top Rated User (1.2m points)

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