Find the basis and dimension for the row space of the following matrix: [begin{pmatrix} 1 & 2 & 3 2 & 4 & 6 3 & 6 & 9 end{pmatrix}]

Question

Find the basis and dimension for the row space of the following matrix: [begin{pmatrix} 1 & 2 & 3  2 & 4 & 6  3 & 6 & 9 end{pmatrix}]

Accepted Answer

Step:1 ：Step 1: Reduce the matrix to row-echelon form. This can be achieved by subtracting the first row from the second and third rows, and then dividing the second and third rows by 1 and 2 respectively: [begin{pmatrix} 1 & 2 & 3  0 & 0 & 0  0 & 0 & 0 end{pmatrix}]Step:2 ：Step 2: Remove the rows of zeros, since they do not contribute to the basis of the row space: [begin{pmatrix} 1 & 2 & 3 end{pmatrix}]Step:3 ：Step 3: The remaining row is a basis for the row space. The dimension is the number of vectors in the basis, which is 1 in this case.

Answer

Step: 1 ：Step 1: Reduce the matrix to row-echelon form. This can be achieved by subtracting the first row from the second and third rows, and then dividing the second and third rows by 1 and 2 respectively: [begin{pmatrix} 1 & 2 & 3  0 & 0 & 0  0 & 0 & 0 end{pmatrix}]Step: 2 ：Step 2: Remove the rows of zeros, since they do not contribute to the basis of the row space: [begin{pmatrix} 1 & 2 & 3 end{pmatrix}]Step: 3 ：Step 3: The remaining row is a basis for the row space. The dimension is the number of vectors in the basis, which is 1 in this case.

Find the basis and dimension for the row space of the following matrix: $(\begin{matrix} 1 & 2 & 3 2 & 4 & 6 3 & 6 & 9 \end{matrix})$

Answer

Popular Problems

Find the basis and dimension for the row space of the following matrix: (123 246 369)

Answer

Popular Problems

Find the basis and dimension for the row space of the following matrix: $(\begin{matrix} 1 & 2 & 3 2 & 4 & 6 3 & 6 & 9 \end{matrix})$