FInd x, y, z, and w
in Trigonometry Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

To use Cramer’s Rule we need to construct a 4×4 matrix based on the coefficients of the 4 variables. But we can simplify this to a 3×3 matrix by noting that z=-y because y+z=0. So z+w=-2 can be replaced by -y+w=-2. We work out the determinant associated with the new coefficient matrix for (w x y):

| 0   1   1 |

| 1   0 -1 |

| 1 -1   0 | which has the value ∆=(0(0-1)-1(0-(-1))+1(-1))=(0-1-1)=-2.

We use this value to find the variables as the common divisor.

w=

|   4   1   1 |

| -2   0 -1 | × -½

|   2 -1   0 |

Note that we omit the constant for the second equation because we already included y+z=0 when we reduced the problem to the new matrix.

Evaluating the determinant we get w=-½(4(-1)-2+2)=2.

x=

| 0   4   1 |

| 1  -2 -1 | × -½

| 1    2  0 |

x=-½(-4+4)=0.

y=

| 0   1   4 |

| 1   0 -2 | × -½

| 1 -1    2 |

y=-½(-4-4)=4

z=-4.

So the solution is (w,x,y,z)=(2,0,4,-4).

by Top Rated User (629k points)

Related questions

1 answer
1 answer
asked Jul 11, 2016 in Other Math Topics by anonymous | 93 views
1 answer
1 answer
asked Dec 2, 2011 in Algebra 2 Answers by anonymous | 298 views
1 answer
asked Feb 26, 2014 in Other Math Topics by Kanabesa Level 1 User (400 points) | 186 views
1 answer
asked Feb 26, 2014 in Other Math Topics by Kanabesa Level 1 User (400 points) | 113 views
1 answer
asked Feb 24, 2014 in Algebra 1 Answers by Kanabesa Level 1 User (400 points) | 151 views
1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
82,584 questions
87,142 answers
1,959 comments
3,703 users