Advertisements
Advertisements
प्रश्न
2x − y = 17
3x + 5y = 6
Advertisements
उत्तर
\[\text{ Given }: 2x - y = 17\]
\[ 3x + 5y = 6\]
Using Cramers Rule, we get
\[D = \begin{vmatrix} 2 & - 1 \\3 & 5 \end{vmatrix} = 10 + 3 = 13\]
\[ D_1 = \begin{vmatrix} 17 & - 1 \\ 6 & 5 \end{vmatrix} = 85 + 6 = 91\]
\[ D_2 = \begin{vmatrix} 2 & 17 \\ 3 & 6 \end{vmatrix} = 12 - 51 = - 39\]
Now,
\[x = \frac{D_1}{D} = \frac{91}{13} = 7\]
\[y = \frac{D_2}{D} = \frac{- 39}{13} = - 3\]
\[ \therefore x = 7\text{ and }y = - 3\]
APPEARS IN
संबंधित प्रश्न
Examine the consistency of the system of equations.
5x − y + 4z = 5
2x + 3y + 5z = 2
5x − 2y + 6z = −1
Solve the system of linear equations using the matrix method.
2x – y = –2
3x + 4y = 3
Evaluate the following determinant:
\[\begin{vmatrix}\cos \theta & - \sin \theta \\ \sin \theta & \cos \theta\end{vmatrix}\]
Evaluate
\[\begin{vmatrix}2 & 3 & - 5 \\ 7 & 1 & - 2 \\ - 3 & 4 & 1\end{vmatrix}\] by two methods.
If \[A = \begin{bmatrix}2 & 5 \\ 2 & 1\end{bmatrix} \text{ and } B = \begin{bmatrix}4 & - 3 \\ 2 & 5\end{bmatrix}\] , verify that |AB| = |A| |B|.
Evaluate the following determinant:
\[\begin{vmatrix}a & h & g \\ h & b & f \\ g & f & c\end{vmatrix}\]
Without expanding, show that the value of the following determinant is zero:
\[\begin{vmatrix}1/a & a^2 & bc \\ 1/b & b^2 & ac \\ 1/c & c^2 & ab\end{vmatrix}\]
Without expanding, show that the value of the following determinant is zero:
\[\begin{vmatrix}\sin^2 23^\circ & \sin^2 67^\circ & \cos180^\circ \\ - \sin^2 67^\circ & - \sin^2 23^\circ & \cos^2 180^\circ \\ \cos180^\circ & \sin^2 23^\circ & \sin^2 67^\circ\end{vmatrix}\]
Evaluate :
\[\begin{vmatrix}x + \lambda & x & x \\ x & x + \lambda & x \\ x & x & x + \lambda\end{vmatrix}\]
Evaluate the following:
\[\begin{vmatrix}a + x & y & z \\ x & a + y & z \\ x & y & a + z\end{vmatrix}\]
Without expanding, prove that
\[\begin{vmatrix}a & b & c \\ x & y & z \\ p & q & r\end{vmatrix} = \begin{vmatrix}x & y & z \\ p & q & r \\ a & b & c\end{vmatrix} = \begin{vmatrix}y & b & q \\ x & a & p \\ z & c & r\end{vmatrix}\]
Find the area of the triangle with vertice at the point:
(2, 7), (1, 1) and (10, 8)
Using determinants show that the following points are collinear:
(3, −2), (8, 8) and (5, 2)
Find the value of x if the area of ∆ is 35 square cms with vertices (x, 4), (2, −6) and (5, 4).
2x − y = 1
7x − 2y = −7
2x − y = − 2
3x + 4y = 3
x − 4y − z = 11
2x − 5y + 2z = 39
− 3x + 2y + z = 1
x − y + 3z = 6
x + 3y − 3z = − 4
5x + 3y + 3z = 10
If A is a singular matrix, then write the value of |A|.
If \[A = \begin{bmatrix}0 & i \\ i & 1\end{bmatrix}\text{ and }B = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}\] , find the value of |A| + |B|.
If \[A = \begin{bmatrix}1 & 2 \\ 3 & - 1\end{bmatrix}\text{ and B} = \begin{bmatrix}1 & - 4 \\ 3 & - 2\end{bmatrix},\text{ find }|AB|\]
If I3 denotes identity matrix of order 3 × 3, write the value of its determinant.
If A and B are non-singular matrices of the same order, write whether AB is singular or non-singular.
There are two values of a which makes the determinant \[∆ = \begin{vmatrix}1 & - 2 & 5 \\ 2 & a & - 1 \\ 0 & 4 & 2a\end{vmatrix}\] equal to 86. The sum of these two values is
Solve the following system of equations by matrix method:
x − y + 2z = 7
3x + 4y − 5z = −5
2x − y + 3z = 12
The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping others and some others (say z) for supervising the workers to keep the colony neat and clean. The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added to two times the number of awardees for honesty is 33. If the sum of the number of awardees for honesty and supervision is twice the number of awardees for helping others, using matrix method, find the number of awardees of each category. Apart from these values, namely, honesty, cooperation and supervision, suggest one more value which the management of the colony must include for awards.
3x − y + 2z = 0
4x + 3y + 3z = 0
5x + 7y + 4z = 0
x + y − 6z = 0
x − y + 2z = 0
−3x + y + 2z = 0
Let a, b, c be positive real numbers. The following system of equations in x, y and z
(a) no solution
(b) unique solution
(c) infinitely many solutions
(d) finitely many solutions
If \[A = \begin{bmatrix}1 & - 2 & 0 \\ 2 & 1 & 3 \\ 0 & - 2 & 1\end{bmatrix}\] ,find A–1 and hence solve the system of equations x – 2y = 10, 2x + y + 3z = 8 and –2y + z = 7.
Three chairs and two tables cost ₹ 1850. Five chairs and three tables cost ₹2850. Find the cost of four chairs and one table by using matrices
Solve the following equations by using inversion method.
x + y + z = −1, x − y + z = 2 and x + y − z = 3
If `|(2x, 5),(8, x)| = |(6, -2),(7, 3)|`, then value of x is ______.
Using determinants, find the equation of the line joining the points (1, 2) and (3, 6).
`abs ((("b" + "c"^2), "a"^2, "bc"),(("c" + "a"^2), "b"^2, "ca"),(("a" + "b"^2), "c"^2, "ab")) =` ____________.
The number of values of k for which the linear equations 4x + ky + 2z = 0, kx + 4y + z = 0 and 2x + 2y + z = 0 possess a non-zero solution is
