IGNOU MTE 2 2026 - Find the solutions to the following system of equations by reduc

Question

Find the solutions to the following system of equations by reducing the corresponding augmented matrix to row-reduced echelon form.

$$\begin{aligned} 2a + 3b + 4c + d &= 8 \\ a + 2b + 2c + 2d &= 3 \\ a - b + c + 3d &= 3 \end{aligned}$

09 Jan 2026

Answer :

Word Count : 512

The given system is 2a + 3b + 4c + d = 8, a + 2b + 2c + 2d = 3, a − b + c + 3d = 3. The corresponding augmented matrix is [ \begin{bmatrix} 2 & 3 & 4 & 1 & | & 8 \ 1 & 2 & 2 & 2 & | & 3 \ 1 & -1 & 1 & 3 & | & 3 \end{bmatrix}. ] Interchange the first and second rows to get a leading 1: [ \begin{bmatrix} 1 & 2 & 2 & 2 & | & 3 \ 2 & 3 & 4 & 1 & | & 8 \ 1 & -1 & 1 & 3 & | & 3 \end{bmatrix}. ] Eliminate the entries below the leading 1 by performing (R_2 \to R_2 - 2R_1) and (R_3 \to R_3 - R_1): [ \begin{bmatrix} 1 & 2 & 2 & 2 & | & 3 \ 0 & -1 & 0 & -3 & | & 2 \ 0 & -3 & -1 & 1 & | & 0 \end{bmatrix}. ] Multiply the second row by −1: [ \begin{bmatrix} 1 & 2 & 2 & 2 &

________ ____ _______ ___ _________ ______ ___ _________ __________ ________.
________ ___ _______ _______ ___ ___ _____ _____ ________ ______ ______.
_____ ________ ________ ____ _______ ___ ___ _______ ______ ________ _________ __________.
_________ ___ _______ ____ ____ _________ ______ _________ ____ ________ ________ _________.
____ ________ ______ ___ _____.
_____ _________ _________ ______ __________ ________ ____ ____ _________ ______.
________ ____ _____ _____ _____ _________ ____ _________ __________ ________ ______.
________ __________ ______ _________ ____ __________ ___ _______ ______ __________ _________.
________ ____ _________ ______ _____ _________ __________ _________.
__________ ________ ___ _______ ______ _______ ______ ______ _______.
______ _______ _______ _________ _____ ___ _________ _________ __________ _______ ________ _________.
_________ __________ ________ ___ ___ __________ ____ ________ _________ ________.
_____ ______ __________ _____ _______ __________ ____ _____.
___ __________ ____ ______ ____ ________.
_____ _________ ________ ____ ____ _________ ___ ___.
____ ____ _________ _____ ____ ______ ____.
_______ __________ __________ ________ _______ _____ _____.
___ __________ ____ ______ __________ ____ ___ ____ _______ ______.
_______ ______ _________ _______ ____ ______ __________ ___ ___ ________.
____ ___ _______ _________ ____ ______ __________ ___ ___ ______.
___ __________ _________ ____ __________ __________ __________ _______ ____ ________ _____.
_______ ____ _________ ____ ___ _________ _________.
___ ___ __________ __________ ____ _______ ___ ___ ____ _____ __________.
________ ______ _______ ____ _________ _________ ________ ___ ________ ______ __________.
_____ _____ _________ ____ _____ _________ ____ _______ ____ ____ ______ _______.
_____ ___ __________ __________ ________ ______ _________ ______ ___ ___ ____.
__________ _______ _______ ________ ________ _____.
_______ ______ ________ ________ _____ ___.
________ ___ ________ ______ _________ ________ ____ ________ ____.
______ _________ __________ ________ _____ ___.
_________ ___ ________ ____ _______ _________ ______ ________ ____ _________ ________ ___.
__________ ______ _________ ________ ____ _____ ___ _____ ______ ______.
_______ ______ __________ ____ _____ ____ _______ _____ _______ ________ _________.
_______ _____.

IGNOU ACADEMY

Your IGNOU journey, made easier.

Solved Assignments
Study Notes
Guess Papers
Question Papers

Call Us WhatsApp

STUDY • PREPARE • SUCCEED

Skip in 10