Let A be an n × n nonsingular matrix. (a) Prove that ( A T ) − 1 = ( A − 1 ) T . (b) Let b be an n - vector ; then A x = b has exactly one solution. Prove that this solution satisfies the normal equations.
Let A be an n × n nonsingular matrix. (a) Prove that ( A T ) − 1 = ( A − 1 ) T . (b) Let b be an n - vector ; then A x = b has exactly one solution. Prove that this solution satisfies the normal equations.
Solution Summary: The author proves that the solution of Ax=B satisfies the normal equations.
Let A be an
n
×
n
nonsingular matrix. (a) Prove that
(
A
T
)
−
1
=
(
A
−
1
)
T
. (b) Let b be an n-vector; then
A
x
=
b
has exactly one solution. Prove that this solution satisfies the normal equations.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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HOW TO FIND DETERMINANT OF 2X2 & 3X3 MATRICES?/MATRICES AND DETERMINANTS CLASS XII 12 CBSE; Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=bnaKGsLYJvQ;License: Standard YouTube License, CC-BY