Explain why the columns of an nxn matrix A span R" when A is invertible. Choose the correct answer below. O A. Since A is invertible, there exists A such that AA=I. Since AA1 =I, the columns of A span R". O B. Since A is invertible, det A is zero. Since det A is zero, the columns of A span R". O C. Since A is invertible, for each b in R" the equation Ax = b has a unique solution. Since the equation Ax = b has a solution for all b in R", the columns of A span R". O D. Since A is invertible, each b is a linear combination of the columns of A. Since each b is a linear combination of the columns of A, the columns of A span R".

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Explain why the columns of an nxn matrix A span R" when A is invertible.
Choose the correct answer below.
O A.
-1
-1
Since A is invertible, there exists A such that AA=I. Since AA=I, the columns of A span R".
O B. Since A is invertible, det A is zero. Since det A is zero, the columns of A span R"
O C. Since A is invertible, for each b in R" the equation Ax = b has a unique solution. Since the equation Ax =b has a solution for all b in R", the columns of A span R".
O D. Since A is invertible, each b is a linear combination of the columns of A. Since each b is a linear combination of the columns of A, the columns of A span R".
Transcribed Image Text:Explain why the columns of an nxn matrix A span R" when A is invertible. Choose the correct answer below. O A. -1 -1 Since A is invertible, there exists A such that AA=I. Since AA=I, the columns of A span R". O B. Since A is invertible, det A is zero. Since det A is zero, the columns of A span R" O C. Since A is invertible, for each b in R" the equation Ax = b has a unique solution. Since the equation Ax =b has a solution for all b in R", the columns of A span R". O D. Since A is invertible, each b is a linear combination of the columns of A. Since each b is a linear combination of the columns of A, the columns of A span R".
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