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Sia

Question
Math
Posted 6 months ago

Determine the value(s) of xx such that
[x21][3232033422][x14]=[0]x=(2,1/6)
\begin{array}{l}
{\left[\begin{array}{lll}
x & 2 & 1
\end{array}\right]\left[\begin{array}{ccc}
3 & 2 & -3 \\
2 & 0 & 3 \\
-3 & 42 & 2
\end{array}\right]\left[\begin{array}{c}
x \\
-1 \\
4
\end{array}\right]=[0]} \\
x=(-2,-1 / 6)
\end{array}


Note: If there is more than one value separate them by commas.
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Answer from Sia
Posted 6 months ago
Solution by Steps
step 1
To find the value(s) of xx, we need to multiply the given matrices and set the product equal to the zero matrix
step 2
The multiplication of the 1x3 matrix [x 2 1][x \ 2 \ 1] with the 3x4 matrix is performed by multiplying each element of the row by the corresponding elements of the columns and summing the results
step 3
The product of the first matrix and the second matrix is a 1x4 matrix. We set each element of this resulting matrix equal to zero
step 4
The first element of the resulting matrix is 3x+43=03x + 4 - 3 = 0
step 5
The second element of the resulting matrix is 2x+0+42=02x + 0 + 42 = 0
step 6
The third element of the resulting matrix is 3x+0+2=0-3x + 0 + 2 = 0
step 7
Solving the first equation 3x+43=03x + 4 - 3 = 0 gives us x=1/3x = -1/3
step 8
Solving the second equation 2x+42=02x + 42 = 0 gives us x=21x = -21
step 9
Solving the third equation 3x+2=0-3x + 2 = 0 gives us x=2/3x = 2/3
step 10
However, xx must satisfy all three equations simultaneously. We find that there is no single value that satisfies all three equations, which means there is an inconsistency in the system
Answer
There is no solution for xx as the system of equations is inconsistent.
Key Concept
Matrix multiplication and solving a system of linear equations
Explanation
The value(s) of xx are determined by solving the system of linear equations obtained from setting the product of the given matrices equal to the zero matrix. However, if the system is inconsistent, as in this case, there is no solution for xx.

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