Examine the Consistency of the Linear System AX = 0 and Solve It

Math Problem Statement

Only from 2nd question onwards and only steps and answer no explanation

Certainly, here are the steps and answers from the 2nd question onwards:

Given matrix $A$ :

1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{bmatrix}$$ 1. **Row operations to get echelon form** (as done previously): $$\begin{bmatrix} 1 & 2 & 3 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$$ 2. **General solution**: $$\begin{aligned} x_1 &= -2t - 3s \\ x_2 &= t \\ x_3 &= s \end{aligned}$$ where $$t$$ and $$s$$ are free parameters. ### Problem 3: Find Rank by Using Normal Form Given matrix $$A$$: $$A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 5 & 6 \end{bmatrix}$$ 1. **Row operation**: $$R_2 \rightarrow R_2 - 2R_1$$ 2. **Normal form**: $$A = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \end{bmatrix}$$ **Rank** = 2.

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Linear Algebra
Systems of Linear Equations

Row Echelon Form
Rank of a Matrix

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