If vectors i+j+2k, i+pj+5k and 5i+3j+4k are linearly dependent, the value of p is what?
Please I'm looking for the explanation. i already know the answer is 2, i just don't know how.

(D) 2

Step-by-step explanation:

If two or more vectors are linearly dependent, then one of them can be expressed as a linear combination of the rest. In other words, vectors are dependent linearly on one another if the determinant of the matrix that they form is zero.

Given vectors:

i+j+2k

i+pj+5k

5i+3j+4k

Now, since they are linearly dependent, then the determinant of their matrix should be zero. i.e

Let their matrix be A and is given by;

A =  

Where;

the first column holds the i components of the vectors

the second column holds the j components of the vectors and

the third column holds the k components of the vectors

=> |A| = det(A) = 0

Now, let's calculate the determinant.

=> 4p -15 - 4 + 25 + 6 - 10p = 0

=> 4p - 10p + 12 = 0

=> 6p = 12

=> p = 2

Therefore, the value of p for which the vectors are linearly dependent is 2

step-by-step explanation:

if x = 2 you have to find x to finish the problem

answer:

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

explanation:

service only with 20% tip  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the  

service

−−−−−−  

so technically the answer is  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

however, the intention of the question provider may have been that your answer is to be  

$

87.12

(

1

+

8

100

)

=

$

94.09

to 2 decimal places.

'

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge  

.

→

$

72.60

20% tip  

20

100

×

$

72.60

=

$

14.52

−−−−−−  

←

add

$

87.12

tax  

8

100

×

$

87.12

=

$

6.97

−−−−−  

←

add

$

94.09

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