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AnnyKZ [126]
3 years ago
15

Suppose a system of linear equations has a 3 5 augmented matrix whose fifth column is a pivot column. is the system consistent?

why (or why not)? 4
Mathematics
1 answer:
likoan [24]3 years ago
7 0

Answer:

The system will be inconsistent.

Step-by-step explanation:

We are given that a system of linear equations has a 3×5 augmented matrix whose fifth column is a pivot column.

Then such a system is not consistent because since the augmented matrix has a pivot in fifth column it means that the new column added to the matrix A will lead to increase in the rank as that of matrix  A.

Hence the rank of A and Augment A will not remain same and hence the system will be inconsistent.

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Step-by-step explanation:

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At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Gnoma [55]

There would be 12 people at the party!

In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.

Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.

This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.

Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.

Hope this helps!

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