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Dafna11 [192]
3 years ago
14

Select four statements from the invertible matrix theorem and show that all four statements are true or false

Mathematics
1 answer:
Lelechka [254]3 years ago
5 0

Answer:

A) A is an invertible matrix ( TRUE )

B) A is a row equivalent to the n x n identity matrix ( n = 3 ) ( TRUE )

C ) The equation Ax = 0 has only the trivial solution ( TRUE )

D ) The columns of A form a linearly independent set ( TRUE )

Step-by-step explanation:

Assuming a matrix A

\left[\begin{array}{ccc}1&2&1\\-1&0&3\\4&1&5\end{array}\right]

det A = 1 [ 0 -3 ] +  2 [12 + 5 ]  + 1[-1]

        = -3 + 34 -1 = 30 ≠ 0

THEREFORE  det A = 30 ≠ 0

Attached is the detailed solution of the given statements above

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