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3x − y + 2z = 3
2x + y + 3z = 5
x − 2y − z = 1
Concept: undefined >> undefined
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3x − y + 2z = 6
2x − y + z = 2
3x + 6y + 5z = 20.
Concept: undefined >> undefined
x − y + z = 3
2x + y − z = 2
− x − 2y + 2z = 1
Concept: undefined >> undefined
x + y − z = 0
x − 2y + z = 0
3x + 6y − 5z = 0
Concept: undefined >> undefined
2x + y − 2z = 4
x − 2y + z = − 2
5x − 5y + z = − 2
Concept: undefined >> undefined
x − y + 3z = 6
x + 3y − 3z = − 4
5x + 3y + 3z = 10
Concept: undefined >> undefined
A salesman has the following record of sales during three months for three items A, B and C which have different rates of commission
| Month | Sale of units | Total commission drawn (in Rs) |
||
| A | B | C | ||
| Jan | 90 | 100 | 20 | 800 |
| Feb | 130 | 50 | 40 | 900 |
| March | 60 | 100 | 30 | 850 |
Find out the rates of commission on items A, B and C by using determinant method.
Concept: undefined >> undefined
An automobile company uses three types of steel S1, S2 and S3 for producing three types of cars C1, C2and C3. Steel requirements (in tons) for each type of cars are given below :
| Cars C1 |
C2 | C3 | |
| Steel S1 | 2 | 3 | 4 |
| S2 | 1 | 1 | 2 |
| S3 | 3 | 2 | 1 |
Using Cramer's rule, find the number of cars of each type which can be produced using 29, 13 and 16 tons of steel of three types respectively.
Concept: undefined >> undefined
Solve each of the following system of homogeneous linear equations.
x + y − 2z = 0
2x + y − 3z = 0
5x + 4y − 9z = 0
Concept: undefined >> undefined
Solve each of the following system of homogeneous linear equations.
2x + 3y + 4z = 0
x + y + z = 0
2x − y + 3z = 0
Concept: undefined >> undefined
Solve each of the following system of homogeneous linear equations.
3x + y + z = 0
x − 4y + 3z = 0
2x + 5y − 2z = 0
Concept: undefined >> undefined
Find the real values of λ for which the following system of linear equations has non-trivial solutions. Also, find the non-trivial solutions
\[2 \lambda x - 2y + 3z = 0\]
\[ x + \lambda y + 2z = 0\]
\[ 2x + \lambda z = 0\]
Concept: undefined >> undefined
If a, b, c are non-zero real numbers and if the system of equations
(a − 1) x = y + z
(b − 1) y = z + x
(c − 1) z = x + y
has a non-trivial solution, then prove that ab + bc + ca = abc.
Concept: undefined >> undefined
If A is a singular matrix, then write the value of |A|.
Concept: undefined >> undefined
For what value of x, the following matrix is singular?
Concept: undefined >> undefined
Write the value of the determinant
\[\begin{bmatrix}2 & 3 & 4 \\ 2x & 3x & 4x \\ 5 & 6 & 8\end{bmatrix} .\]
Concept: undefined >> undefined
State whether the matrix
\[\begin{bmatrix}2 & 3 \\ 6 & 4\end{bmatrix}\] is singular or non-singular.
Concept: undefined >> undefined
Find the value of the determinant
\[\begin{bmatrix}4200 & 4201 \\ 4205 & 4203\end{bmatrix}\]
Concept: undefined >> undefined
