SOLUTION: Given the linear system
X + 2y = 1O
3x + (6 + t)y = 30,
(a) Determine a particular value oft so that the system
has infinitely many solutions.
(b) Determine a particular value
Algebra ->
Matrices-and-determiminant
-> SOLUTION: Given the linear system
X + 2y = 1O
3x + (6 + t)y = 30,
(a) Determine a particular value oft so that the system
has infinitely many solutions.
(b) Determine a particular value
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Question 1175505: Given the linear system
X + 2y = 1O
3x + (6 + t)y = 30,
(a) Determine a particular value oft so that the system
has infinitely many solutions.
(b) Determine a particular value oft so that the system
has a unique solution.
(c) How many different values of t can be selected in
part (b)?
You can put this solution on YOUR website! Given the linear system
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(a) Determine a particular value of t so that the system
has infinitely many solutions.
Lines that lay right on top of each other; the linear system has infinitely many solutions, basically it's same line
first equation have and second equation have , first equation have constant term and second equation have => so, multiplied by
then must be ->-> ..........
-----------------------------
------------------------=>the linear system has many solutions
(b) Determine a particular value oft so that the system
has a unique solution.
could any number except ..........let's take
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(c) How many different values of can be selected in
part (b)?
The extended matrix of the system is
.
(a) the system has infinitely many solutions, if and only if both lines of the coefficient matrix are proportional.
From the form of the matrix, it is clear that the only value of "t" for it is t= 0.
(b) For all other values of "t" the lines of the matrix are not proportional
Hence, for all values of "t" different from t= 0, the system has a unique solution.
(c) In part (b), there are infinitely many possible values of "t".
