Let Abe an n × n matrix. Prove that the followingstatements are equivalent. (a) N ( A ) = { 0 } . (b) A is nonsingular. (c) For each b ∈ ℝ n , the system A x = b has aunique solution.
Let Abe an n × n matrix. Prove that the followingstatements are equivalent. (a) N ( A ) = { 0 } . (b) A is nonsingular. (c) For each b ∈ ℝ n , the system A x = b has aunique solution.
Solution Summary: The author explains how the system Ax=b has a unique solution to prove that A is non-singular.
Let Abe an
n
×
n
matrix. Prove that the followingstatements are equivalent. (a)
N
(
A
)
=
{
0
}
. (b) A is nonsingular. (c) For each
b
∈
ℝ
n
, the system
A
x
=
b
has aunique solution.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.