SOLUTION: use properties of determinants to find the value of each determinant if it is know that |x y z| |u v w| |1 2 3| =4 |x y z| |u v w| |2 4 6|

Algebra ->  Matrices-and-determiminant -> SOLUTION: use properties of determinants to find the value of each determinant if it is know that |x y z| |u v w| |1 2 3| =4 |x y z| |u v w| |2 4 6|      Log On


   

Question 188320This question is from textbook
: use properties of determinants to find the value of each determinant if it is know that
|x y z|
|u v w|
|1 2 3| =4


|x y z|
|u v w|
|2 4 6| This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, you can multiply a scalar value "k" by any row of a determinant like this:

Note: you can pick any row. In this example, I'm using the first row.




abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C1%2C2%2C3%29%29=4 Start with the given equation.


Since the bottom row of the resulting determinant is 2, 4, and 6 this means that this row is 2 times the bottom row of the given determinant.



2%2Aabs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C1%2C2%2C3%29%29=2%2A4 Multiply both sides by 2


abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C2%2A1%2C2%2A2%2C2%2A3%29%29=2%2A4 Multiply the scalar 2 by the entire bottom row of the determinant


abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C2%2C4%2C6%29%29=8 Multiply



So the answer is abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C2%2C4%2C6%29%29=8