Describe all solutions of Ax=0 in parametric vector form, where A is row equival

Maui1opj

Maui1opj

Answered question

2023-03-30

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix
[13042608]

Answer & Explanation

pandurorc2x

pandurorc2x

Beginner2023-03-31Added 3 answers

To find all solutions of the equation Ax=0, where A is row equivalent to the matrix [13042608], we need to find the parametric vector form of the solutions.
We can start by performing row reduction on the augmented matrix [13042608].
Applying row operations, we obtain the row-reduced form:
[13040000]
The second row indicates that we have a free variable. Let's call it t.
Now, we can express the solutions in terms of the free variable t. Rewriting the row-reduced form as equations, we have:
x+3y4z=0
0=0
We can solve the first equation for x:
x=3y+4z
Expressing the solution in vector form, we have:
[xyz]=[3y+4zyz]=y[310]+z[401]
Therefore, the solutions of the equation Ax=0 in parametric vector form are:
[xyz]=y[310]+z[401]
where y and z are real numbers that serve as parameters.

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