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34kurt
3 years ago
9

Suppose the solutions of a homogeneous system of six linear equations in nine unknowns are all linear combination of four linear

ly independent nonzero solutions. Will the system necessarily have a solution for every possible choice of constants on the right sides of the equations? Explain.
Mathematics
1 answer:
lesantik [10]3 years ago
3 0

Answer:

yes, system have a solution

Step-by-step explanation:

Given data

linear equation = 6

unknown = 9

to find out

Will the system necessarily have a solution

solution

we multiply one non zero solution and we know that

A = 6 × 9 matrix

and n = 9

so dim (NulA) = 3  

because we know (9-6) = 3

and rank of (A) =  n - dim(NulA) = 9 - 3  = 6

so we say now here image of A i.e  6 dimensional subspace (A have 6 row)

so that Col (A) will be R^{6}

so its mean Ax = b has solution when we have b

so we now say that yes, system have a solution

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Solve 9x^2- 17x- 85 = 0 Give your solutions correct to 3 significant figures.​
dybincka [34]

Answer:

x =\frac{17}{18} +\frac{1}{18} \sqrt{3349} OR x =\frac{17}{18} +\frac{-1}{18} \sqrt{3349}

Step-by-step explanation:

9x2−17x−85=0

For this equation: a=9, b=-17, c=-85

9x2+−17x+−85=0

Step 1: Use quadratic formula with a=9, b=-17, c=-85.

x =\frac{-b + \sqrt{b^{2}-4ac } }{2a}

x  =\frac{-(-17)+\sqrt{(-17)^{2} -4(9)(-85)} }{2(9)}

x =\frac{17}{18} +\frac{-1}{18} \sqrt{3349}

4 0
2 years ago
Liam wants to buy a Nintendo Switch. The Switch costs $350 plus tax. He has $380. If tax is 9%, will he have enough to buy the S
goldenfox [79]

Step-by-step explanation:

I'm not a 100 % sure but 350.00 x 0.06 =21 so 350 +21 = 371.00

4 0
2 years ago
Read 2 more answers
6.
user100 [1]

Answer:

A. y = –5x – 27

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line parallel to  y = − 5 x + 3 .

y = − 5 x − 27                           PARALLEL

...................................................................................................................................................

Find the negative reciprocal of the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line perpendicular to  y = − 5 x + 3 .

y = 1 /5 x + 21 /5                    PERPENDICULAR

7 0
2 years ago
If f(x)=3<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D" id="TexFormula1" title="x^{2}" alt="x^{2}" align="absmiddle" class="late
Anvisha [2.4K]

Answer:

\sf f(-3) = 23

<u>given:</u>

\sf f(x) = 3x^2 -4

to find the output, replace x with the given integer.

solve:

\sf f(-3) = 3(-3)^2 -4

\sf f(-3) = 3(9) -4

\sf f(-3) = 27 -4

\sf f(-3) = 23

5 0
2 years ago
If you flip three fair coins, what is the probability that you’ll get all three heads?
Sladkaya [172]

Answer:

3/6

Step-by-step explanation:

no idea if its right

5 0
3 years ago
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