Let A be a 4 × 3 matrixand let b ∈ ℝ 4 . Howmanypossible solutions could the system A x = b have if N ( A ) = { 0 } ? Answer the same question in the case N ( A ) ≠ { 0 } . Explain your answers.
Let A be a 4 × 3 matrixand let b ∈ ℝ 4 . Howmanypossible solutions could the system A x = b have if N ( A ) = { 0 } ? Answer the same question in the case N ( A ) ≠ { 0 } . Explain your answers.
Solution Summary: The author explains how each solution of the system Ax = b can be written as a sum y + z.
Let A be a
4
×
3
matrixand let
b
∈
ℝ
4
. Howmanypossible solutions could the system
A
x
=
b
have if
N
(
A
)
=
{
0
}
? Answer the same question in the case
N
(
A
)
≠
{
0
}
. Explain your answers.
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