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Nikitich [7]
3 years ago
5

Which property is illustrated by the equation 3(mn)=(3m)n?

Mathematics
2 answers:
yKpoI14uk [10]3 years ago
5 0
Associative property of multiplication
...........................................................
Elenna [48]3 years ago
3 0
That would be the associative property
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Question 1 (5 points): Consider the system of linear equations x1 − 4x2 − x4 = −7 x2 − 2x4 = 3 x4 + 2x5 = 3 (a) Write down the c
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Answer:

Step-by-step explanation:

Given is a system of equations as

x1-4x2 - x4 = -7\\ \\x2 - 2x4 = 3 \\\\x4 + 2x5 = 3

We have 5 variables and 3 equations

a) coefficient matrix of this system is

1   -4   0   -1   0\\

0    1   0   -2   0\\

0    0   0    1    2\\

We find that x3 has no coefficient in any of the equations so we can omit x3 and write as equations for 4 variables as

1   -4     -1   0\\

0    1     -2   0\\

0    0     1    2\\

b) Augmented matrix is

1   -4     -1   0\\  7

0    1     -2   0\\ 3

0    0     1    2\\3

c) For row operations to ehelon form

we can do R1+4R2 = R1

We get

1   0   -9  0 \\  19

0   1  -2   0 \\   3

0   0   1   2  \\   3

Now let us do R1 = R1+9R3 and R2 = R2+2R3

1  0   0   0  \\ 46

0  1   0   0   \\  9

0   0  1   2   \\  3

d) We find that there are infinite solutions to  the system in parametric form, since x4 and x5 are linked with only one equation

e) x1 = 46, x2 = 9, x4+2x5 =3

Or x1 =46, x2 =9, x4 = 3-2x5, x5 = x5 is the parametric solution

 

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