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Matrix
- Thread starter Sailboat
- Start date
arthur ohlsten
Full Member
- Joined
- Feb 20, 2005
- Messages
- 852
Write the equations as two matrices A=K
A is a 6x7 and K is a 6x1
I have placed a letter over each column to help in writing the matrices
...n...m...p...s...t....x...j
...5...0...0...0....0...0..-1
..-4...5...0...0....0...0...0
...0..-4...5...0....0...0...0
...0...0..-4...5....0...0...0
...0...0...0..-5....5...0...0
...0...0...0...0....4..-5...0
K
-1
-1
-1
-1
-1
.0
you have two matrices a 6 row 7 columns, and a 6row 1 column
Do row opoerations on the 6x7 to form a main diagonal of 1. Do the operations on both matrices simultaneously. In other words 6 multiplications and subtractions
You should have the last row of the 6x7 with a x term and the 6th row of the 6x1 matrix with a valu then you have x = a value.
Arthur
A is a 6x7 and K is a 6x1
I have placed a letter over each column to help in writing the matrices
...n...m...p...s...t....x...j
...5...0...0...0....0...0..-1
..-4...5...0...0....0...0...0
...0..-4...5...0....0...0...0
...0...0..-4...5....0...0...0
...0...0...0..-5....5...0...0
...0...0...0...0....4..-5...0
K
-1
-1
-1
-1
-1
.0
you have two matrices a 6 row 7 columns, and a 6row 1 column
Do row opoerations on the 6x7 to form a main diagonal of 1. Do the operations on both matrices simultaneously. In other words 6 multiplications and subtractions
You should have the last row of the 6x7 with a x term and the 6th row of the 6x1 matrix with a valu then you have x = a value.
Arthur
Hello, Sailboat!
We have:
. . \(\displaystyle \begin{array}{ccccccccc} j &&\text{-}5n &&&&& = & 1 \\ & 5m & \text{-}4n &&&&& = & \text{-}1 \\ & 4m && \text{-}5p &&&& = & 1 \\ &&& 4p & \text{-5}s &&& = & 1 \\ &&&& 5s & \text{-}5t && = & 1 \\ &&&&& 4t & \text{-}5x &=& 0 \end{array}\)
The matrix is:
. . \(\displaystyle \left|\begin{array}{ccccccc|c} 1 & 0 &\text{-}5 & 0 & 0 & 0 & 0 & 1 \\ 0 & 5 & \text{-}4 & 0 & 0 & 0 & 0 & \text{-}1 \\ 0 & 4 & 0 & \text{-}5 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 4 & \text{-}5 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 5 & \text{-}5 &0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 4 & \text{-}5 & 0 \end{array}\right|\)
Bon voyage!
I would like to solve the system of equations using a matrix.
. . . \(\displaystyle \begin{array}{ccc}5n+1&=& j \\5m+1&=&4n \\5p+1&=&4m \\ 5s+1&=&4p \\ 5t+1&=&5s \\ 4t&=&5x\end{array}\)
We have:
. . \(\displaystyle \begin{array}{ccccccccc} j &&\text{-}5n &&&&& = & 1 \\ & 5m & \text{-}4n &&&&& = & \text{-}1 \\ & 4m && \text{-}5p &&&& = & 1 \\ &&& 4p & \text{-5}s &&& = & 1 \\ &&&& 5s & \text{-}5t && = & 1 \\ &&&&& 4t & \text{-}5x &=& 0 \end{array}\)
The matrix is:
. . \(\displaystyle \left|\begin{array}{ccccccc|c} 1 & 0 &\text{-}5 & 0 & 0 & 0 & 0 & 1 \\ 0 & 5 & \text{-}4 & 0 & 0 & 0 & 0 & \text{-}1 \\ 0 & 4 & 0 & \text{-}5 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 4 & \text{-}5 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 5 & \text{-}5 &0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 4 & \text{-}5 & 0 \end{array}\right|\)
Bon voyage!