SOLVED:Can any system of linear equations be written as an augmented matrix? Explain why or why not. Explain how to write that augmented matrix.
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SOLVED:Can any system of linear equations be written as an augmented matrix? Explain why or why not. Explain how to write that augmented matrix.
VIDEO ANSWER: so we went to the trimming. Whether or not we can read an earlier question, this is any system of linear equations, a documented mind tricks matr…
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Augmented Matrix Examples
SOLVED:The augmented matrices that follow are in row echelon form. For each case, indicate whether the corresponding linear system is consistent. If the system has a unique solution, find it. (a) ( 1 2 4 0 1 3 0 0 1) (b) ( 1 3 1 0 1 -1 0 0 0) (c) ( 1 -2 4 1 0 0 1 3 0 0 0 0) (d) ( 1 -2 2 -2 0 1 -1 3 0 0 1 2) (e) ( 1 3
SOLVED:The augmented matrices that follow are in row echelon form. For each case, indicate whether the corresponding linear system is consistent. If the system has a unique solution, find it. (a) ( 1 2 4 0 1 3 0 0 1) (b) ( 1 3 1 0 1 -1 0 0 0) (c) ( 1 -2 4 1 0 0 1 3 0 0 0 0) (d) ( 1 -2 2 -2 0 1 -1 3 0 0 1 2) (e) ( 1 3
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SOLVED:Write the augmented matrix corresponding to the system of equations. 2 x-3 y+z =1 -x+y-4 z =-3 3 x-z =2
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SOLVED:Write the augmented matrix corresponding to the system of equations. 2 x-3 y+z =1 -x+y-4 z =-3 3 x-z =2
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The classical way to invert a matrix A in a basic linear algebra course augments A by the n ×n identity matrix I and applies the Gauss-Jordan algorithm of Exercise 2 to this augmented matrix (including the solution part, i.e., the division by the pivots .ak k^(n-1)). Then A^-1 shows up where I initially was. How many floating point operations are required for this method? Compare this to the operation count of (8)/(3) n^3 𝒪(n^2) required for the same task using LU decomposition (see Example 5.5
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