Determine whether the statement below is true or false. Justify the answer. Here, A is an mxn matrix. The dimension of Nul A is the number of variables in the equation Ax = 0. Choose the correct answer below. O A. The statement is true. The number of total variables involved in solving the equation Ax = 0 is the dimension of Nul A. B. The statement is false. The dimension of Nul A is the number of variables in the equation Ax = 0 minus the number of free variables in the equation Ax = 0. c. The statement is true. The dimension of Nul A is the same as the amount of vectors in the set x = {x1.X,} that satisfy the equation Ax = 0. D. The statement is false. The dimension of Nul A is the number of free variables in the equation Ax = 0.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Determine whether the statement below is true or false. Justify the answer. Here, A is an mxn matrix.
The dimension of Nul A is the number of variables in the equation Ax = 0.
Choose the correct answer below.
O A. The statement is true. The number of total variables involved in solving the equation Ax = 0 is the dimension of Nul A.
B. The statement is false. The dimension of Nul A is the number of variables in the equation Ax = 0 minus the number of free variables in the
equation Ax = 0.
c. The statement is true. The dimension of Nul A is the same as the amount of vectors in the set x = {x1.X,} that satisfy the equation
Ax = 0.
D. The statement is false. The dimension of Nul A is the number of free variables in the equation Ax = 0.
Transcribed Image Text:Determine whether the statement below is true or false. Justify the answer. Here, A is an mxn matrix. The dimension of Nul A is the number of variables in the equation Ax = 0. Choose the correct answer below. O A. The statement is true. The number of total variables involved in solving the equation Ax = 0 is the dimension of Nul A. B. The statement is false. The dimension of Nul A is the number of variables in the equation Ax = 0 minus the number of free variables in the equation Ax = 0. c. The statement is true. The dimension of Nul A is the same as the amount of vectors in the set x = {x1.X,} that satisfy the equation Ax = 0. D. The statement is false. The dimension of Nul A is the number of free variables in the equation Ax = 0.
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