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The solution of the following system of equation is
2x + 3y = 5
5x – 2y = 3
2x + 3y = 5
Multiply equation with ‘5’, we get
10x + 15y = 25……………………(1)
5x – 2y = 3
Multiply equation with ‘2’, we get
10x  4y = 6………………………(2)
Subtracting (1) from (2), we get
19y = 19
y = 1
Put the value of y in eq(1)
10x + 15(1) = 25
10x = 10
x = 1
One third of sum of two angles is 60° and one fourth of their difference is 28°. The angles are
Solution:
Let the two angles be 'x' and 'y'.
So, according to the question,
One third of the sum of two angles : 1/3(x+y) = 60
x/3 + y/3 = 60 ......(1)
Quarter of their difference : 1/4(xy) = 28
x/4  y/4 = 28...........(2)
Multiplying the equation (1) by 3 and equation (2) by 4, we get
x + y =180 .......(3) x  y = 112 ......(4)
Subtracting (4) from (3),
x + y = 180
x  y = 112
 + 
_________
2y = 68
_________
2y = 68
y = 34
Putting the value of y = 34 in the equation (3)
x + y = 180
x + 34 = 180
x = 180  34
x = 146
The two angles are 146° and 34°.
For a square matrix A in a matrix equation AX = B, if │A│≠ 0, then
The following system of equations has
x + 3y + 3z = 2
x + 4y + 3z = 1
x + 3y + 4z = 2
Let A = {(1,3,3) (1,4,3) (1,3,4)}
A = 1(169) 3(43) +3(34)
A = 1(7) 3(1) +3(1)
= 7  3  3
= 1
Therefore, A is not equal to zero, it has unique solution.
Inverse of matrix (A^{1}) = (adj A)/A
The system of equations kx + 2y – z = 1,
(k – 1)y – 2z = 2
(k + 2)z = 3 has a unique solution, if k is
This system of equations has a unique solution, if
System of equations AX = B is inconsistent if
If (adj A) B ≠ 0 (zero matrix), then the solution does not exist. The system of equations is inconsistent. Else, if (adj A) B = 0 then the system will either have infinitely many solutions (consistent system) or no solution (inconsistent system).
A = {(6,7) (8,9)}
A = (6 * 9)  (8 * 7)
= 54  56
A = 2
A^{1} = ½{(9,7) (8,6)}
A^{1} = {(9/2, 7/2) (4,3)}
A system of linear equations AX = B is said to be inconsistent, if the system of equations has
A linear system is said to be consistent if it has at least one solution; and is said to be inconsistent if it has no solution. have no solution, a unique solution, and infinitely many solutions, respectively.
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209 videos218 docs139 tests
