Given a matrix A = (begin{bmatrix} 2 & 4 & 1 1 & 2 & 1 3 & 6 & 2 end{bmatrix}), find the null space.

Question

Given a matrix A = (begin{bmatrix} 2 & 4 & 1  1 & 2 & 1  3 & 6 & 2 end{bmatrix}), find the null space.

Accepted Answer

Step:1 ：Step 1: Find the row reduced echelon form (RREF) of the matrix. [ RREF = begin{bmatrix} 1 & 2 & 0  0 & 0 & 1  0 & 0 & 0 end{bmatrix} ] Step:2 ：Step 2: From RREF, the system of equations is [begin{cases} x + 2y = 0  z = 0 end{cases}] Step:3 ：Step 3: Solving the system, we get [begin{cases} x = -2y  z = 0 end{cases}]

Answer

Step: 1 ：Step 1: Find the row reduced echelon form (RREF) of the matrix. [ RREF = begin{bmatrix} 1 & 2 & 0  0 & 0 & 1  0 & 0 & 0 end{bmatrix} ] Step: 2 ：Step 2: From RREF, the system of equations is [begin{cases} x + 2y = 0  z = 0 end{cases}] Step: 3 ：Step 3: Solving the system, we get [begin{cases} x = -2y  z = 0 end{cases}]

Given a matrix A = \(\begin{bmatrix} 2 & 4 & 1 \ 1 & 2 & 1 \ 3 & 6 & 2 \end{bmatrix}\), find the null space.

Answer

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