Question

# 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 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. 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.  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5