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Radda [10]
3 years ago
9

Find the determinant of the nxn matrix A with 5's on the diagonal, l's above the diagonal, and O's below the diagonal. det (A) =

Mathematics
1 answer:
Vilka [71]3 years ago
6 0

Answer:

n times 5

Step-by-step explanation:

A matrix Anxn of this way is called an upper triangular matrix. It can be proved that the determinant of this kind of matrix is  

a_{11}+a_{22}+...+a_{nn}

In this case, it would be 5+5+...+5 (n times) = n times 5

We are going to develop each determinant by the first column taking as pivot points the elements of the diagonal

det\left[\begin{array}{cccc}5&a_{12}&a_{13}...&a_{1n}\\0&5&a_{23}...&a_{2n}\\...&...&...&...\\0&0&0&5\end{array}\right] =5+det\left[\begin{array}{ccc}5&a_{23}...&a_{2n}\\0&5&a_{3n}\\...&...&...\\0&0&5\end{array}\right]=5+5+...+det\left[\begin{array}{cc}5&a_{n-1,n}\\0&5\end{array}\right]=5+5+...+5+5\;(n\;times)

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3 years ago
5% of what number is 85?
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5% = 0.5

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Divide by 0.5

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8 0
3 years ago
Hi I need help with this
ch4aika [34]

Answer:

well this is going to be long, but

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7. -9.111

8. -7.833

9. 17/25

10. -1/100

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13. 3 1/200

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15. -9 49/50

16. -10 113/250

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Step-by-step explanation:

sorry i didnt know which question you needed help on so i did it all, hope this helped you!! have a great day

4 0
2 years ago
mr albernathy perchases a selection of wrenches for his shop. his bill was $78. he buys the same number of $1.50 wrenches and $2
ICE Princess25 [194]

Answer:

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Step-by-step explanation:

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2 years ago
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melomori [17]

Answer:

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Step-by-step explanation:

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(3x - 1)(4x - 3)

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8 0
2 years ago
Read 2 more answers
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