Given the matrix A = begin{bmatrix} 1 & 2 & 3 2 & 4 & 6 3 & 6 & 9 end{bmatrix}, find the basis and dimension for the row space of the matrix.

Question

Given the matrix A = begin{bmatrix} 1 & 2 & 3  2 & 4 & 6  3 & 6 & 9 end{bmatrix}, find the basis and dimension for the row space of the matrix.

Accepted Answer

Step:1 ：Step 1: Perform row operations to bring the matrix to row-echelon form. This does not change the row space. We subtract twice the first row from the second, and thrice the first row from the third to get: A = begin{bmatrix} 1 & 2 & 3  0 & 0 & 0  0 & 0 & 0 end{bmatrix}Step:2 ：Step 2: The row space of this matrix is the span of the non-zero rows. So, the basis for the row space of the original matrix is the set {begin{bmatrix} 1 & 2 & 3 end{bmatrix}}Step:3 ：Step 3: The dimension of the row space is the number of vectors in the basis. So, the dimension of the row space of the matrix is 1.

Answer

Step: 1 ：Step 1: Perform row operations to bring the matrix to row-echelon form. This does not change the row space. We subtract twice the first row from the second, and thrice the first row from the third to get: A = begin{bmatrix} 1 & 2 & 3  0 & 0 & 0  0 & 0 & 0 end{bmatrix}Step: 2 ：Step 2: The row space of this matrix is the span of the non-zero rows. So, the basis for the row space of the original matrix is the set {begin{bmatrix} 1 & 2 & 3 end{bmatrix}}Step: 3 ：Step 3: The dimension of the row space is the number of vectors in the basis. So, the dimension of the row space of the matrix is 1.

Given the matrix $A = [\begin{matrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{matrix}]$ , find the basis and dimension for the row space of the matrix.

Answer

Popular Problems

Given the matrix A=[123246369], find the basis and dimension for the row space of the matrix.

Answer

Popular Problems

Given the matrix $A = [\begin{matrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{matrix}]$ , find the basis and dimension for the row space of the matrix.