In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads toa)Lower triangular matrixb)Diagonal matrixc)Upper triangular matrixd)Singular matrix
Question
In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads toa)Lower triangular matrixb)Diagonal matrixc)Upper triangular matrixd)Singular matrix
Solution
The Gauss elimination method for solving a system of linear algebraic equations leads to an upper triangular matrix. So, the correct answer is c) Upper triangular matrix.
Here are the steps of the Gauss elimination method:
- Write the system of equations in matrix form.
- Perform row operations to form an upper triangular matrix. This process is called triangularization or pivoting.
- Once the upper triangular matrix is formed, start the back substitution process to find the variables.
The upper triangular matrix is a special type of square matrix, where all the entries below the main diagonal are zero.
Similar Questions
In solving simultaneous equations by Gauss - Jordan method, the coefficient matrix is reduced toa)Diagonal Matrixb)Null Matrixc)Square Matrixd)Unit Matrix
Which operation can be used in Gauss elimination method?a)Elementary row operationsb)Multiplicationc)Additiond)Elementary column operation
In solving simultaneous equations by Gauss - Jordan method, the coefficient matrix is reduced to
Consider a system of linear equations for price P and production Q as follows: 5P+Q=68, and -3P+Q=-10. Its coefficient matrix is given by \left[\begin{array}{ccc} 5&1&68 \\ -3&1&-10\end{array}\right] . Now, use forward elimination method to obtain its upper triangular form \left[\begin{array}{ccc} 1&a&13.6 \\ 0&1&19.25\end{array}\right] where a is some value you need to work out. So, what is the value of a rounded to 2 decimal places? Question 5 Answer a. 0.20 b. 0.00 c. 19.25 d. none of the others e. 0.36
GAUSSIAN ELIMINATION
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