Advertisements
Advertisements
प्रश्न
Find the area of the triangle with vertice at the point:
(−1, −8), (−2, −3) and (3, 2)
Advertisements
उत्तर
\[∆ = \frac{1}{2}\begin{vmatrix}- 1 & - 8 & 1 \\ - 2 & - 3 & 1 \\ 3 & 2 & 1\end{vmatrix} \]
\[ ∆ = \frac{1}{2}\begin{vmatrix}- 1 & - 8 & 1 \\ - 1 & 5 & 0 \\ 3 & 2 & 1\end{vmatrix} \left[\text{ Applying }R_2 \to R_2 - R_1 \right]\]
\[ ∆ = \frac{1}{2}\begin{vmatrix}- 1 & - 8 & 1 \\ - 1 & 5 & 0 \\ 4 & 10 & 0\end{vmatrix} \left[\text{ Applying }R_3 \to R_3 - R_1 \right]\]
\[ ∆ = \frac{1}{2}\begin{vmatrix}- 1 & 5 \\ 4 & 10\end{vmatrix}\]
\[ ∆ = \frac{1}{2}\left| - 10 - 20 \right|\]
\[ ∆ = \frac{1}{2}\left( 30 \right) = 15\text{ square units }\]
APPEARS IN
संबंधित प्रश्न
Find the value of a if `[[a-b,2a+c],[2a-b,3c+d]]=[[-1,5],[0,13]]`
Evaluate
\[∆ = \begin{vmatrix}0 & \sin \alpha & - \cos \alpha \\ - \sin \alpha & 0 & \sin \beta \\ \cos \alpha & - \sin \beta & 0\end{vmatrix}\]
Evaluate the following determinant:
\[\begin{vmatrix}6 & - 3 & 2 \\ 2 & - 1 & 2 \\ - 10 & 5 & 2\end{vmatrix}\]
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:
\[\begin{vmatrix}1 & 43 & 6 \\ 7 & 35 & 4 \\ 3 & 17 & 2\end{vmatrix}\]
Show that x = 2 is a root of the equation
If \[a, b\] and c are all non-zero and
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:
(1, −1), (2, 1) and (4, 5)
Using determinants show that the following points are collinear:
(2, 3), (−1, −2) and (5, 8)
Using determinants prove that the points (a, b), (a', b') and (a − a', b − b') are collinear if ab' = a'b.
If the points (3, −2), (x, 2), (8, 8) are collinear, find x using determinant.
2x − y = 1
7x − 2y = −7
Prove that :
Prove that :
Prove that :
3x + y = 19
3x − y = 23
2x − 3y − 4z = 29
− 2x + 5y − z = − 15
3x − y + 5z = − 11
x + 2y = 5
3x + 6y = 15
Solve each of the following system of homogeneous linear equations.
2x + 3y + 4z = 0
x + y + z = 0
2x − y + 3z = 0
Find the value of the determinant \[\begin{vmatrix}2^2 & 2^3 & 2^4 \\ 2^3 & 2^4 & 2^5 \\ 2^4 & 2^5 & 2^6\end{vmatrix}\].
If \[\begin{vmatrix}2x + 5 & 3 \\ 5x + 2 & 9\end{vmatrix} = 0\]
If \[\begin{vmatrix}2x & 5 \\ 8 & x\end{vmatrix} = \begin{vmatrix}6 & - 2 \\ 7 & 3\end{vmatrix}\] , write the value of x.
If \[∆_1 = \begin{vmatrix}1 & 1 & 1 \\ a & b & c \\ a^2 & b^2 & c^2\end{vmatrix}, ∆_2 = \begin{vmatrix}1 & bc & a \\ 1 & ca & b \\ 1 & ab & c\end{vmatrix},\text{ then }\]}
Solve the following system of equations by matrix method:
5x + 7y + 2 = 0
4x + 6y + 3 = 0
Solve the following system of equations by matrix method:
x + y + z = 6
x + 2z = 7
3x + y + z = 12
Show that the following systems of linear equations is consistent and also find their solutions:
6x + 4y = 2
9x + 6y = 3
Show that each one of the following systems of linear equation is inconsistent:
x + y − 2z = 5
x − 2y + z = −2
−2x + y + z = 4
A company produces three products every day. Their production on a certain day is 45 tons. It is found that the production of third product exceeds the production of first product by 8 tons while the total production of first and third product is twice the production of second product. Determine the production level of each product using matrix method.
x + y − 6z = 0
x − y + 2z = 0
−3x + y + 2z = 0
If \[\begin{bmatrix}1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & - 1\end{bmatrix}\begin{bmatrix}x \\ y \\ z\end{bmatrix} = \begin{bmatrix}1 \\ 0 \\ 1\end{bmatrix}\], find x, y and z.
For the system of equations:
x + 2y + 3z = 1
2x + y + 3z = 2
5x + 5y + 9z = 4
If ` abs((1 + "a"^2 "x", (1 + "b"^2)"x", (1 + "c"^2)"x"),((1 + "a"^2) "x", 1 + "b"^2 "x", (1 + "c"^2) "x"), ((1 + "a"^2) "x", (1 + "b"^2) "x", 1 + "c"^2 "x"))`, then f(x) is apolynomial of degree ____________.
If A = `[(1,-1,0),(2,3,4),(0,1,2)]` and B = `[(2,2,-4),(-4,2,-4),(2,-1,5)]`, then:
A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is
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
If the system of equations x + λy + 2 = 0, λx + y – 2 = 0, λx + λy + 3 = 0 is consistent, then
