Mth501 Assignment No. 1 solution
Tuesday, April 12, 2011 Posted In Mth Edit This
Maximum Marks: 25
Due Date: 12 April, 2011
INSTRUCTIONS
Please read the following instructions before attempting the solution of this assignment:
• To solve this assignment, you should have good command over 01-08 lectures.
In order to solve this assignment you have strong concepts about following topics
ü Introduction to Matrices.
ü Echelon and Reduced Echelon Form.
ü System of Linear Equation.
ü Dependence of Sets.
Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in these lectures.
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Question: 1 Marks: 10
If 
and 
. Using the Reduced Row Echelon Form method, determine whether 
is in 
?
and . Using the Reduced Row Echelon Form method, determine whether is in ?Question: 2 Marks: 05
Determine without solving, whether the following sets of vectors are linearly independent or dependent. Justify your answer with appropriate reason.
Question: 3 Marks: 10
If is the augmented matrix of a consistent linear system then find the value(s) of ‘
’ using the Row Echelon Form method.
:::::::::::::::::::::::::::::::::::::::
’ using the Row Echelon Form method. :::::::::::::::::::::::::::::::::::::::
Question 1:
is mein aap ko yeh show karna hai k kia ham a ko x aur y k linear combination mein likh saktay hain..
i.e. aap ko yeh wali 2 equations solve karni hain row reduced echelon form ki madad se...
x+3y=5 and 2x+4y=10
agar in equations ka solution exist karta hai, tou answer YES hai, otherwise NO
Question 2
(a) Dependent (because if we write given vectors in matrix form and row reduce the given matrix, then two free variables will always exist because of the fact that variables are 4 but number of rows are 2. Therefore, at most two basic variables can exist and at least 2 free variables will always exist, and when free variable exists, then it is linearly DEPENDENT
(b) Remember, jab koi bhi aik vector ALL ZERO ho tou us case mein linearly DEPENDENT hota hai.... yahan par third vector ALL ZERO hai, tou is liay DEPENDENT answer aaye ga
(c) independent because none of the vectors is a constant multiple of another
Question (3)
yeh bahut straight forward hai, agar aap ko row reduced echelon form theek tarah samajh aayi hooi hai, tou aap yeh aasani se kar saktay ho...aap ko given augmeted matrix ko row reduce karna paray ga...aur phir aakhir mein equations ko combine karna paray ga, aur wahan se h ki value nikalni paray gi..
Solution:
is mein aap ko yeh show karna hai k kia ham a ko x aur y k linear combination mein likh saktay hain..
i.e. aap ko yeh wali 2 equations solve karni hain row reduced echelon form ki madad se...
x+3y=5 and 2x+4y=10
agar in equations ka solution exist karta hai, tou answer YES hai, otherwise NO
Question 2
(a) Dependent (because if we write given vectors in matrix form and row reduce the given matrix, then two free variables will always exist because of the fact that variables are 4 but number of rows are 2. Therefore, at most two basic variables can exist and at least 2 free variables will always exist, and when free variable exists, then it is linearly DEPENDENT
(b) Remember, jab koi bhi aik vector ALL ZERO ho tou us case mein linearly DEPENDENT hota hai.... yahan par third vector ALL ZERO hai, tou is liay DEPENDENT answer aaye ga
(c) independent because none of the vectors is a constant multiple of another
Question (3)
yeh bahut straight forward hai, agar aap ko row reduced echelon form theek tarah samajh aayi hooi hai, tou aap yeh aasani se kar saktay ho...aap ko given augmeted matrix ko row reduce karna paray ga...aur phir aakhir mein equations ko combine karna paray ga, aur wahan se h ki value nikalni paray gi..
Solution:
