- #1
henry3369
- 194
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I'm trying to learn column space currently and I'm confused about the meaning of rows and columns.
So I'm given this definition for column space:
"The column space of matrix A is the set Col A of all linear combinations of the columns of A"
Given the matrix A:
[ 1 -3 -4 ]
[ -4 6 -2 ]
[ -3 7 6 ]
b=
[ 3 ]
[ 3 ]
[ -4 ]
Determine if b is in the column space of A.
My books solves by row reducing [ A b ].
Has this always been what I was solving for whenever I row reduced an augmented matrix to obtain x for Ax = b?
For example, when I'm given a system of linear equation such as:
2x1 + 3x2 = 5
1x1 + 2x2 = 3
and I have to solve for x.
Do the columns of the coefficient matrix of this system of linear equation, have the same meaning as the matrix above, vectors?
So I'm given this definition for column space:
"The column space of matrix A is the set Col A of all linear combinations of the columns of A"
Given the matrix A:
[ 1 -3 -4 ]
[ -4 6 -2 ]
[ -3 7 6 ]
b=
[ 3 ]
[ 3 ]
[ -4 ]
Determine if b is in the column space of A.
My books solves by row reducing [ A b ].
Has this always been what I was solving for whenever I row reduced an augmented matrix to obtain x for Ax = b?
For example, when I'm given a system of linear equation such as:
2x1 + 3x2 = 5
1x1 + 2x2 = 3
and I have to solve for x.
Do the columns of the coefficient matrix of this system of linear equation, have the same meaning as the matrix above, vectors?