Question
Find the solutions to the following system of equations by reducing the corresponding augmented matrix to row-reduced echelon form.
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 _____ ______ __________ ________ ___ ______ __________ ____ ___ __________ _______ ______.
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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 _____ ______ __________ ________ ___ ______ __________ ____ ___ __________ _______ ______.
________ _______ _______ _______ _____ ______ ______.
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