Question

Complex Analysis

Suppose H is an nxn matrix. If the equation Hx = c is inconsistent for some c in R", what can you say about the equation Hx = 0? Why?

O B. The statement that Hx = c is inconsistent for some c is equivalent to the statement that Hx = c has no solution for some c. From this, all of the statements in the Inyertible Matrix Theorem are false, including the statement that Hx 0 has only the trivial solution. Thus, Hx =0 has no solution.

O C. The statement that Hx = c is inconsistent for some c is equivalent to the statement that Hx = c has a solution for every c. From this, all of the statements in the Invertible Matrix Theorem are true, including the statement that Hx =0 has only the trivial solution.

. The statement that Hx =c is inconsistent for some c is equivalent to the statement that Hx c has a solution for every c. From this, all of the statements in the Invertible Matrix Theorem are true, including the statement that the columns of H form a linearly independent set. Thus, Hx = 0 has an infinite number of solutions.

O A. The statement that Hx = c is inconsistent for some c is equivalent to the statement that Hx = c has no solution for some c. From this, all of the statements in the Invertible Matrix Theorem are false, including the statement that Hx = 0 has only the trivial solution. Thus, Hx = 0 has a nontrivial solution.


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