Use Theorem 3 to prove Theorem 16 . THEOREM 3: Let C d be an m × ( n + 1 ) matrix in reduced echelon form, where C d represents a consistent system. Let C d have r nonzero rows. Then r ≤ n and in the solution of the system there are n - r variables that can be assigned arbitrary values. THEOREM 16: Let A be an ( n × n ) marix. Then A is nonsingular if and only if A is row equivalent to I .
Use Theorem 3 to prove Theorem 16 . THEOREM 3: Let C d be an m × ( n + 1 ) matrix in reduced echelon form, where C d represents a consistent system. Let C d have r nonzero rows. Then r ≤ n and in the solution of the system there are n - r variables that can be assigned arbitrary values. THEOREM 16: Let A be an ( n × n ) marix. Then A is nonsingular if and only if A is row equivalent to I .
Solution Summary: The author proves that A is nonsingular if and only when it is row equivalent to I using the Theorem 3.
THEOREM 3: Let
C
d
be an
m
×
(
n
+
1
)
matrix in reduced echelon form, where
C
d
represents a consistent system. Let
C
d
have
r
nonzero rows. Then
r
≤
n
and in the solution of the system there are
n
-
r
variables that can be assigned arbitrary values.
THEOREM 16: Let
A
be an
(
n
×
n
)
marix. Then
A
is nonsingular if and only if
A
is row equivalent to
I
.
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY