Engineering Mathematics Miscellaneous
- The solution to the system of equations is
2 5 x = 2 -4 3 y -30
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Equations from this matrix are:
2x + 5y = 2 and – 4x + 3y = – 30
By solving these two equations, we get x = 6; y = – 2Correct Option: D
Equations from this matrix are:
2x + 5y = 2 and – 4x + 3y = – 30
By solving these two equations, we get x = 6; y = – 2
- x + 2y + z = 4
2x + y + 2z = 5
x – y + z = 1
The system of algebraic given below has
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ρ [A] = [ A / B ] = 2
But ρ [A] = ρ [A / B ] < Number of variables.
ρ < n
So we have infinite number of solutions.Correct Option: C
ρ [A] = [ A / B ] = 2
But ρ [A] = ρ [A / B ] < Number of variables.
ρ < n
So we have infinite number of solutions.
- Consider the following system of equations
2x1 + x2 + x3 = 0
x2 – x3 = 0
x1 + x2 = 0
this system has
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Rank of [A] = 2
Rank of [A / B] = 2
Since Rank of [A] = Rank of [A / B ] < 3
So infinite number of solutions are obtained.Correct Option: C
Rank of [A] = 2
Rank of [A / B] = 2
Since Rank of [A] = Rank of [A / B ] < 3
So infinite number of solutions are obtained.
- For what value of a, if any, will the following system of equation in x, y and z have a solution?
2x + 3y = 4
x + y + z = 4
x + 2y – z = a
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Augmented matrix is
R1 → R1 – 2R2
R3 → R3 – R2
R1 → R1 – R3
will have solution if a = 0
as Rank of [A] = Rank of Augmented [A]Correct Option: B
Augmented matrix is
R1 → R1 – 2R2
R3 → R3 – R2
R1 → R1 – R3
will have solution if a = 0
as Rank of [A] = Rank of Augmented [A]
- With a 1 unit change in b, what is the change in x in the solution of the system of equations x + y = 2, 1.01x + 0.99 y = b?
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Given x + y = 2 ...(i)
1.01 x + 0.99 y = b... (ii)
Multiply 0.99 with equation (i), and substract from equation (ii); we get
(1.01 – 0.99)x = 1.98
∴ 0.02 ∆b∴ ∆x = 1 = 50 units 0.02 Correct Option: C
Given x + y = 2 ...(i)
1.01 x + 0.99 y = b... (ii)
Multiply 0.99 with equation (i), and substract from equation (ii); we get
(1.01 – 0.99)x = 1.98
∴ 0.02 ∆b∴ ∆x = 1 = 50 units 0.02