First slide

System of linear equations

Question

The system $A X = B$ of $n$ equation in $n$ unknowns has infinitely many solutions, if

Easy

A

$\det A \neq 0$
B

$(a d j A) B \neq O$
C

$\det A = 0$
D

$(a d j A) B = O$

Solution

$X = A^{- 1} B$
$\Rightarrow X = \frac{(a d j A) B}{| A |}$

Clearly, if the system has infinite solutions $| A | = 0 a n d (a d j A) B = 0$

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