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The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
The correct option will be Option C: x=5t-3
y=4t-5
z=t
where t is the real number.
A matrix is in row echelon form when the first non-zero number from the left i.e. leading coefficient is always to right of the first non-zero number in the row above and rows consisting of all zeros are at bottom of the matrix.
The row echelon form of the matrix is given in the question.
from row-echelon form of the matrix, we can write the equation as,
x-5z=-3
y-4z=-5
Let's assume z=t, where t is the real number
now we can find x and y by putting z=t in the equation
x-5t=-3
⇒x=-3+5t
y-4t=-5
y=-5+4t
Now we get the solution of x,y,z in terms of t
x=5t-3
y=4t-5
z=t
where t is the real number.
So the correct option will be Option C: x=5t-3
y=4t-5
z=t
where t is the real number.
Learn more about row-echelon form
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