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Test: System of Linear Equations - Question 1

If the system

2x – y + 3z = 2

x + y + 2z = 2

5x – y + az = b

Has infinitely many solutions, then the values of a and b, respectively, are

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Test: System of Linear Equations - Question 2

For what value of μ do the simultaneous equations 5x + 7y = 2, 15x + 21y = μ have no solution?

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*Answer can only contain numeric values

Test: System of Linear Equations - Question 3

Gauss-Seidel method is used to solve the following equations (as per the given order):

x_{1} + 2x_{2} + 3x_{3} = 5

2x_{1} + 3x_{2} + x_{3} = 1

3x_{1} + 2x_{2} + x_{3} = 3

Assuming initial guess as x_{1} = x_{2} = x_{3} = 0, the value of x_{3} after the first iteration is ________

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Test: System of Linear Equations - Question 4

The value of k, for which the following system of linear equations has a non-trivial solution.

x + 2y - 3z = 0

2x + y + z = 0

x - y + kz = 0

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Test: System of Linear Equations - Question 5

For what value of λ, do the simultaneous equation 2x + 3y = 1, 4x + 6y = λ have infinite solutions?

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Test: System of Linear Equations - Question 6

For what value of k, the system linear equation has **no** solution

(3k + 1)x + 3y - 2 = 0

(k^{2} + 1)x + (k - 2)y - 5 = 0

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Test: System of Linear Equations - Question 7

The value of k for which the system of equations x + ky + 3z = 0, 4x + 3y + kz = 0, 2x + y + 2z = 0 has non-trivial solution is

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*Answer can only contain numeric values

Test: System of Linear Equations - Question 8

Consider matrix The number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________

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Test: System of Linear Equations - Question 9

The set of equations

x + y + z = 1

ax – ay + 3z = 5

5x – 3y + az = 6

has infinite solutions, if a =

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*Answer can only contain numeric values

Test: System of Linear Equations - Question 10

Consider the system of equations The value of x_{3} (round off to the nearest integer), is ______.

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Test: System of Linear Equations - Question 11

The approximate solution of the system of simultaneous equations

2x - 5y + 3z = 7

x + 4y - 2z = 3

2x + 3y + z = 2

by applying Gauss-Seidel method one time (using initial approximation as x - 0, y - 0, z - 0) will be:

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Test: System of Linear Equations - Question 12

A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain a unique solution by multiplying both left and right sides of the equation by A^{T} (the super script T denotes the transpose) and inverting the matrix A^{T} A?

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Test: System of Linear Equations - Question 14

Consider a matrix

The matrix A satisfies the equation 6A^{-1} = A^{2} + cA + dI, where c and d are scalars and I is the identity matrix. Then (c + d) is equal to

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Test: System of Linear Equations - Question 15

The system of linear equations

-y + z = 0

(4d - 1) x + y + Z = 0

(4d - 1) z = 0

has a non-trivial solution, if d equals

Detailed Solution for Test: System of Linear Equations - Question 15

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