11Involves Cramer's rule........but i don't remember it exactly
lAl=0 => something
lAl ≠0 => something else
Consider a system of linear eqn in 3 variables:
a1x+b1y+c1z=d1
a2x+b2y+c2z=d2
a3x+b3y+c2z=d3
The system can be expressed by matrix eqn
a1 b1 c1 x d1
a2 b2 c2 y = d2
a3 b3 c3 z d3
If A is non singular matrix i.e detA≠0,then soln of abbove system can be found by X=A-1B
If A is singular matrix i.e detA=0,then system will have no unique solution if (adjA)B=0 and the system has no solution if (adjA)B≠0
Consider the following matrices and answer the questions that follow:
A=a 1 0
1 b d
1 b c
B=a 1 1
0 d c
U=f
g
h
V=a2
0
0
X=x
y
z
Q1The system AX=U has infinetly many soln if_______
Q2If AX=U has infinte soln then prove that BX=V has either infinite soln or no soln
Q3If AX=U has infinite soln then determine the condition at which BX=V is consistent.
Q4Assertion/Reason
A:If AX=U has infinite solution and cf≠0 then one solution of BX=V is (0,0,0)
R:If a system has infinite solution,then one solution must be trivial.
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16 Answers
11
33if you forgot cramers or any other rule...
solve it like a layman... convert it to system of equations and solve it...as you used to do in 9th 10th class... no need for matrix concepts..if u are not comfortable with matrices...
11Q4, BX exists but has order 2x1......and V has order 3x1 [7]
So BX cannot b equal to V [7]
pls correct me if i'm wrong
1see your study material da i dont know what it means but i guess it can be used over here ??sry if mistaken..
you will understand see i also studied from that
btw how did you do in the all india test...
11hehe.............
machan neeye sollu da..... BX oda order 2x1 dhane. Aana V oda order 3x1 da
11Pls someone........In Q4
Order of B is 2x3
Order of X is 3x1
So order of BX is 2x1
But how can this matrix be equal to a matrix of order 3x1 ??
Bhaiya, atleast u clear my doubt[2][2]
11So Q4, A is wrong. So automatically R has to be correct [3]
Eureka, pls see the question yaar. BX=V comes in Q2, 3 and 4. PLs see if there is any mistake in the book from which you took this problem from