Consider the 2 × 2 system a 11 x 1 + a 12 x 2 = b 1 a 21 x 1 + a 22 x 2 = b 2 . Show that if a 11 a 22 - a 12 a 21 ≠ 0 , then this system is equivalent to a system of the form c 11 x 1 + c 12 x 2 = d 1 c 22 x 2 = d 2 , Where c 11 ≠ 0 and c 22 ≠ 0 . Note that the second system always has a solution. [ Hint: First suppose that a 11 ≠ 0 , and then consider the special case in which a 11 = 0 .]
Consider the 2 × 2 system a 11 x 1 + a 12 x 2 = b 1 a 21 x 1 + a 22 x 2 = b 2 . Show that if a 11 a 22 - a 12 a 21 ≠ 0 , then this system is equivalent to a system of the form c 11 x 1 + c 12 x 2 = d 1 c 22 x 2 = d 2 , Where c 11 ≠ 0 and c 22 ≠ 0 . Note that the second system always has a solution. [ Hint: First suppose that a 11 ≠ 0 , and then consider the special case in which a 11 = 0 .]
Solution Summary: The author explains that the (2times 2) system is equivalent to a system of the form
Show that if
a
11
a
22
-
a
12
a
21
≠
0
, then this system is equivalent to a system of the form
c
11
x
1
+
c
12
x
2
=
d
1
c
22
x
2
=
d
2
,
Where
c
11
≠
0
and
c
22
≠
0
. Note that the second system always has a solution. [Hint: First suppose that
a
11
≠
0
, and then consider the special case in which
a
11
=
0
.]
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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