Rank of a Matrix using row echelon form
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- เผยแพร่เมื่อ 29 ก.ย. 2024
- Discussed definition of rank of a matrix using echelon form and also discussed few examples to find rank using row echelon form
Check your knowledge with mcqs quiz on rank topic visit: mathematika111.blogspot.com
Nice and easily can understand
J
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DEPARTMENT OF ECONOMICS ) Group Assignment-II
LINEAR ALGEBRA (Econ-2012 Instructor: Abdela U.
1. What is the largest possible number of pivots a 4X6 matrix can have? Why?
2. What is the largest possible number of pivots a 6X4 matrix can have? Why?
3. How many solutions does a consistent linear system of 3 equations and 4 unknowns have? Why?
4. Suppose the coefficient matrix corresponding to a linear system is 4X6 and has 3 pivot columns. How many pivot columns does the augmented matrix have if the linear system is inconsistent?
5. Are the rows independent in each of the following? a)(\begin{matrix}24&8\\ 9&-3\end{matrix})
c)(\begin{matrix}0&4\\ 3&2\end{matrix})
b)(\begin{matrix}2&0\\ 0&2\end{matrix})
d) (\begin{matrix}-1&5\\ 2&-10\end{matrix})
6. Find the rank of each of the following matrices from its echelon matrix, and comment on the question .
al(\begin{matrix}1&5&1\\ 0&3&9\\ -1&0&0\end{matrix})
c\}(\begin{matrix}7&6&3&3\\ 0&1&2&1\\ 8&0&0&8\end{matrix})
d)(\begin{matrix}2&7&9&-1\\ 1&1&0&1\\ 0&5&9&-3\end{matrix})
b)(\begin{matrix}0&-1&-4\\ 3&1&2\\ 6&1&0\end{matrix})
7. Determine whether each matrix is in reduced row-echelon form a\}(\begin{matrix}1&6&5&23\\ 0&1&42&-31\\ 0&0&0&0\end{matrix}) b](\begin{matrix}1&0&0&10\\ 0&0&0&-2\\ 0&0&1&0\\ 0&0&0&0\\ 0&0&0&0\end{matrix}). c]=(\begin{matrix}1&0&0&0\\ 0&1&0&1\\ 0&0&1&5\end{matrix})
d1(\begin{matrix}7&6&3&3\\ 0&1&2&1\\ 8&0&0&8\end{matrix}) ej=(\begin{matrix}1&0&0&0\\ 0&0&0&0\\ 0&1&0&0\end{matrix})
f:(\begin{matrix}1&4\\ 0&0\end{matrix})
8. Use the row reduction algorithm and obtain an equivalent reduced row echelon form to the following matrices ii.&(\begin{matrix}0&3&7&12\\ 8&1&0&1\\ 4&0&1&5\end{matrix})
L.=(\begin{matrix}8&12&3&10\\ 6&-3&7&-2\\ 4&23&1&0\\ 11&9&46&2\\ 8&1&5&-7\end{matrix}).
9. Determine whether the following matrices are positive definite, positive semidefinite,
negative definite, negative semidefinite, or indefinite. A=(\begin{matrix}-2&0&-1\\ 0&-2&-1\\ -2&-4&-3\end{matrix}) B=(\begin{matrix}-2&4&-1\\ 4&-2&-1\\ -1&-1&-2\end{matrix}) E=(\begin{matrix}-2&1&-1\\ 1&-3&-2\\ -1&-2&-5\end{matrix}) C=(\begin{matrix}2&1&-1\\ 1&4&-2\\ -1&-2&4\end{matrix})
D=(\begin{matrix}2&-1&3\\ -1&5&3\\ 3&3&9\end{matrix})
10. Determine of the following quadratic form using a)-2x_{1}^{2}+4x_{1}x_{2}-2x b)5x_{1}^{2}+4x_{2}^{2}+3x_{3}^{2}+2x_{1}x_{2}-5x_{2}x_{3}
She is a model to other teachers.Numero uno.
Nice Video..taught me well
the rank is correct but still it's not entirely row-echelon form
the one you are talking about is row reduced echelon form, where all the leading entries are 1
Hi