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Sagot :
The explicit description of null A by listing vectors that span the null space.
[tex]\left[\begin{array}{ccc}{7} &&&{-4} \\{1} \\{0} \end{array}\right] \left[\begin{array}{ccc}{-6} &&&{2} \\{0} \\{1} \end{array}\right][/tex]
What is the Matrix Vector?
We are given the matrix vector;
[1 3 5 0]
[0 1 4 -2]
Now, let's find the general Ax = 0 solution for the free variables. Thus;
[A, 0] =
[1 3 5 0]
[0 1 4 -2]
Thus;
R₁ → R₁ - 3R₂
⇒ [1 0 -7 6 0]
[0 1 4 -2 0]
The general solution is:
x₁ = 7x₃ - 6x₄
x₂ = -4x₃ + 2x₄
x₃ and x₄ are free variables
x = [tex]\left[\begin{array}{ccc}x_{1} &&&x_{2} \\x_{3} \\x_{4} \end{array}\right][/tex] = [tex]x_{3} \left[\begin{array}{ccc}{7} &&&{-4} \\{1} \\{0} \end{array}\right] + x_{4} \left[\begin{array}{ccc}{-6} &&&{2} \\{0} \\{1} \end{array}\right][/tex]
Thus, Null A is;
[tex]\left[\begin{array}{ccc}{7} &&&{-4} \\{1} \\{0} \end{array}\right] \left[\begin{array}{ccc}{-6} &&&{2} \\{0} \\{1} \end{array}\right][/tex]
Read more about Matrix Vector at; https://brainly.com/question/19202525
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