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Question 1117197: Find the value of k which matrix is
|2. - 10 - 1, 1 2k+3 1, 4 3 2|=75
Found 2 solutions by ikleyn, stanbon:
Answer by ikleyn(52886)   (Show Source):
You can put this solution on YOUR website! .
* * * If your goal is to learn on how to do it, then read the lesson
- Determinant of a 3x3 matrix
in this site.
Then calculate the determinant as the function of "k".
Then solve the linear equation det (M) = 75,
where M is your matrix and det (M) is its determinant expressed as the function of "k".
* * * If your goal is different, then ignore my post.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"3x3-Matrices, determinants, Cramer's rule for systems in three unknowns"
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Find the value of k which matrix is
2 - 10 -1
1 2k+3 1
4 3 2 =75
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2*2k+3*2 + 1*3*-1 + 4*1*-10 - [-1*(2k+3)*4 + 1*3*2 + 2*1*-10]
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= 8k+12 -3 -40 - [-8k-12 +6 - 20]
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= 8k-31 - [-8k-26]
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16k -5 = 75
16k = 80
k = 5
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Cheers,
Stan H.
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