Which of the following are linear equations in x1, x2 and x3?
(a) x1 + 5x2 − (2^0.5)x3 =1
(b) x1 + 3x2 + x1.x3 = 2
(c) x1 = −7x2 + 3x3
(d) x1^−2 + x2 + 8x3 =5
(e) x1^3/5 − 2x2 + x3 = 4
(f) πx1 − (2^0.5)x2 + 13x3 = 7^1/3
a, c, f
cara pengerjaannya ?
Let me put on my clown nose and answer this for you!
The linear equations in x1, x2, and x3 are:
(a) x1 + 5x2 − (2^0.5)x3 = 1
(c) x1 = −7x2 + 3x3
(f) πx1 − (2^0.5)x2 + 13x3 = 7^(1/3)
Why did I choose these equations? Well, they are linear because the highest power of any variable is 1 (no squared or cubed terms) and there are no products of variables. So they fit the criteria!
Now, I hope my clown humor made answering this question a bit more entertaining for you! If you have any more questions, feel free to ask!
To determine whether each equation is linear in x1, x2, and x3, we need to verify if each term in the equation is a linear function of these variables.
A linear equation is one in which each term is either a constant or a constant multiplied by a variable. It does not involve any exponentiation, division, or multiplication of variables together.
Let's analyze each equation to see if it meets the criteria:
(a) x1 + 5x2 - (2^0.5)x3 = 1
This equation is linear because each term is either a constant (1) or a constant multiplied by a variable (x1, x2, x3), without any exponentiation or division.
(b) x1 + 3x2 + x1.x3 = 2
This equation is not linear because it contains a term x1.x3 where x1 and x3 are multiplied together. Linear equations do not involve the multiplication of variables together.
(c) x1 = -7x2 + 3x3
This equation is linear since each term is a constant (-7, 3) multiplied by a variable (x1, x2, x3), without any exponentiation or division.
(d) x1^-2 + x2 + 8x3 = 5
This equation is not linear because it contains a term x1^-2 where x1 is raised to the power of -2. Linear equations do not involve exponentiation of variables.
(e) x1^(3/5) - 2x2 + x3 = 4
This equation is not linear because it contains a term x1^(3/5) where x1 is raised to the power of 3/5. Linear equations do not involve exponentiation of variables.
(f) πx1 - (2^0.5)x2 + 13x3 = 7^(1/3)
This equation is linear because each term is either a constant (π, 7^(1/3)) or a constant multiplied by a variable (x1, x2, x3), without any exponentiation or division.
In summary, the linear equations among the given options are:
(a) x1 + 5x2 - (2^0.5)x3 = 1
(c) x1 = -7x2 + 3x3
(f) πx1 - (2^0.5)x2 + 13x3 = 7^(1/3)