Identify the COLUMN SPACE and the NULL SPACE of the matrix below giving a basis for each if possible.
[1 2 0 0] first row
[5 10 0 0] second row
[0 0 1 1] third row
[0 0 1 1] forth row
thank you!
Transcribed Image Text:The image displays a matrix labeled as \( A \). The matrix is a 4x4 structure written on graph paper. Here is the matrix transcription:
\[
A = \begin{bmatrix}
1 & 2 & 0 & 0 \\
5 & 10 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 1 & 1 \\
\end{bmatrix}
\]
This matrix contains four rows and four columns, with elements as follows:
- First row: 1, 2, 0, 0
- Second row: 5, 10, 0, 0
- Third row: 0, 0, 1, 0
- Fourth row: 0, 0, 1, 1
This setup is often used in mathematical concepts such as systems of equations, transformations, or other areas in linear algebra.
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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![The image displays a matrix labeled as \( A \). The matrix is a 4x4 structure written on graph paper. Here is the matrix transcription:
\[
A = \begin{bmatrix}
1 & 2 & 0 & 0 \\
5 & 10 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 1 & 1 \\
\end{bmatrix}
\]
This matrix contains four rows and four columns, with elements as follows:
- First row: 1, 2, 0, 0
- Second row: 5, 10, 0, 0
- Third row: 0, 0, 1, 0
- Fourth row: 0, 0, 1, 1
This setup is often used in mathematical concepts such as systems of equations, transformations, or other areas in linear algebra.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47978d15-e20a-4071-98c6-506c77d70e17%2F2f7f98a9-6088-4f16-bf7b-2558400cf730%2Fcep93ni_processed.png&w=3840&q=75)
