# Elementary row reduction for an $n\times n$ matrix

$$A= \begin{bmatrix} 1 & 1 & 1 & ... & 1 \\ 1 & 3 & 3 & ... & 3 \\ 1 & 3 & 6 & ... & 6 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & 3 & 6 & ... & 3(n-1) \end{bmatrix}$$

(a) Use the appropriate row replacement operations to zero out the first pivot then use the appropriate row replacement operations to zero out the second pivot column.

(b) Observe the resulting matrix from (a) is a block matrix of the form:

$$A = \begin{bmatrix} X & Y \\ 0 & Z \end{bmatrix}$$

State your resulting matrix for X, Y, and Z.

(c) Based on your result from (b), give a detailed set of steps to find $det(Z)$. [HINT: Take out a scaling factor for Z first then find $det(Z)$.]

Arnomk

44

## Answer

**Answers can be viewed only if**

- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.

1 Attachment

Erdos

4.5K

The answer is accepted.

Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.

- answered
- 476 views
- $35.00

### Related Questions

- Find $x$ so that $\begin{pmatrix} 1 & 0 & c \\ 0 & a & -b \\ -\frac{1}{a} & x & x^2 \end{pmatrix}$ is invertible
- How do I evaluate and interpret these sets of vectors and their geometric descriptions?
- Frontal solver by Bruce Irons? Am I using the right Algorithm here?
- few questions with Matrices
- Closest Points on Two Lines: How to use algebra on equations to isolate unknowns?
- inverse of matrices
- Let $H$ be the subset of all 3x3 matrices that satisfy $A^T$ = $-A$. Carefully prove that $H$ is a subspace of $M_{3x3} $ . Then find a basis for $H$.
- [Linear Algebra] Spectrum