SOLUTION: Use properties of determinants to find the value of the second determinant, if the value of the first is known? | x y z | | u v w | | 1 -2 4 | = 54 | 1 -2 4 | | u v w

Algebra ->  Matrices-and-determiminant -> SOLUTION: Use properties of determinants to find the value of the second determinant, if the value of the first is known? | x y z | | u v w | | 1 -2 4 | = 54 | 1 -2 4 | | u v w       Log On


   

Question 964191: Use properties of determinants to find the value of the second determinant, if the value of the first is known?
| x y z |
| u v w |
| 1 -2 4 | = 54
| 1 -2 4 |
| u v w |
| z y z |
Having a really hard time with this one. Can someone walk me through it? Much appreciated!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28matrix%283%2C3%2C1%2C-2%2C4%2Cu%2Cv%2Cw%2Cz%2Cy%2Cz%29%29 or abs%28matrix%283%2C3%2C1%2C-2%2C4%2Cu%2Cv%2Cw%2C+x%2Cy%2Cz%29%29 ?
Maybe one of the properties of determinants that you were taught is that if you interchange 2 rows (or two columns) the determinant changes sign.
So, if
abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C1%2C-2%2C4%29%29=54 , then abs%28matrix%283%2C3%2C1%2C-2%2C4%2Cu%2Cv%2Cw%2C+x%2Cy%2Cz%29%29=-54 .