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## In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to

In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to

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In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to

Question

A Diagonal matrix B

Lower triangular matrix

C

Upper triangular matrix

D Singular matrix Open in App Solution

The correct option is **C** Upper triangular matrix

Ingauss eliminatipn method for solving system of linear algebraic equation, the equation are reduce to an equivalent upper-triagular matrix.

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SIMILAR QUESTIONS

**Q.**

Solve the following pair of linear equations by the elimination method and the substitution method:

**Q.**There are three

**a**lgebraic methods for solving a pair of linear equation in two variables.

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## [Solved] In the solution of simultaneous equations by the Gauss elimi

Explanation: Gauss elimination method: It is a method to solve the linear system of the form Ax = b, by bringing an augmented matrix into the upper triangle

Home Engineering Mathematics Linear Algebra Matrix Algebra Operations on Matrix

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## In the solution of simultaneous equations by the Gauss elimination method for solving equations, triangularization leads to

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singular matrix

upper triangular matrix

diagonal matrix

lower triangular matrix

## Answer (Detailed Solution Below)

Option 2 : upper triangular matrix

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## Detailed Solution

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**Explanation:**

**Gauss elimination method:**

It is a method to solve the **linear system** of the form Ax = b, by bringing an **augmented matrix into the upper triangle matrix.**

**For example:**Solve, y + Z = 2, 2X + 3Z = 5, X + Y + Z = 3

The** augmented matrix** of the given equations is

= [011220351113] = [203501121113]

Interchanging R1 and R2

= [10325201121113] R1 -----> R1/2 = [103252011201−1212] R3 -------> -R1 +R3 =

[103252011200−32−32]

R3 -------> -R2 + R3

= [10325201120011] R3 --------> -2R2/3

This is the **upper triangular matrix** after various operations.

So, By comparing we get

Z = 1, y +Z = 2, X+32Z=52

**So, The values are x = 1, y = 1, z = 1**

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## Multiple Choice Questions (MCQ) and answers on Numerical Methods

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**Multiple Choice Questions (MCQ) and answers on Numerical Methods**

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