मराठी

सी. बी. एस. ई.वाणिज्य (इंग्रजी माध्यम) इयत्ता १२

प्रश्नपत्रिका

प्रश्नपत्रिका२४८९

पाठ्यपुस्तक उत्तरे२०२१६

MCQ ऑनलाइन सराव परीक्षा४२

महत्वाचे प्रश्न आणि उत्तरे१८८७३

संकल्पना स्पष्टीकरण आणि व्हिडिओ२४२

टाइम टेबल२३

अभ्यासक्रम

Using Determinants, Find the Equation of the Line Joining the Points (3, 1) and (9, 3) - Mathematics

Advertisements

Advertisements

प्रश्न

Using determinants, find the equation of the line joining the points

(3, 1) and (9, 3)

उत्तर

Given: A = (3, 1) and B = (9, 3)

Let the point P be (x, y). So,
Area of triangle ABP = 0

$\Rightarrow ∆ = \frac{1}{2} | \begin{matrix} 3 & 1 & 1 \\ 9 & 3 & 1 \\ x & y & 1 \end{matrix} | = 0$
$\Rightarrow 3 (3 - y) - 1 (9 - x) + 1 (9 y - 3 x) = 0$
$\Rightarrow 9 - 3 y - 9 + x + 9 y - 3 x = 0$
$\Rightarrow - 2 x + 6 y = 0$
$\Rightarrow x = 3 y$

shaalaa.com

Applications of Determinants and Matrices

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 12.2 Q 12.1 Q 13.1

पाठ 6: Determinants - Exercise 6.3 [पृष्ठ ७२]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12

पाठ 6 Determinants
Exercise 6.3 | Q 12.2 | पृष्ठ ७२

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

view
व्हिडिओ ट्यूटोरियल For All Subjects
Applications of Determinants and Matrices

video tutorial00:15:29
Applications of Determinants and Matrices

video tutorial00:27:00
Applications of Determinants and Matrices

video tutorial00:36:09
Applications of Determinants and Matrices

video tutorial00:11:34
Applications of Determinants and Matrices

video tutorial00:23:43

संबंधित प्रश्‍न

Solve system of linear equations, using matrix method.

4x – 3y = 3

3x – 5y = 7

Solve system of linear equations, using matrix method.

2x + y + z = 1

x – 2y – z = $\frac{3}{2}$

3y – 5z = 9

Solve the system of linear equations using the matrix method.

x − y + 2z = 7

3x + 4y − 5z = −5

2x − y + 3z = 12

Evaluate the following determinant:

$| \begin{matrix} 67 & 19 & 21 \\ 39 & 13 & 14 \\ 81 & 24 & 26 \end{matrix} |$

Without expanding, show that the value of the following determinant is zero:

$| \begin{matrix} 8 & 2 & 7 \\ 12 & 3 & 5 \\ 16 & 4 & 3 \end{matrix} |$

Without expanding, show that the value of the following determinant is zero:

$| \begin{matrix} 6 & - 3 & 2 \\ 2 & - 1 & 2 \\ - 10 & 5 & 2 \end{matrix} |$

Without expanding, show that the value of the following determinant is zero:

$| \begin{matrix} 0 & x & y \\ - x & 0 & z \\ - y & - z & 0 \end{matrix} |$

Without expanding, show that the value of the following determinant is zero:

$| \begin{matrix} 1 & 43 & 6 \\ 7 & 35 & 4 \\ 3 & 17 & 2 \end{matrix} |$

Without expanding, show that the value of the following determinant is zero:

$| \begin{matrix} 1^{2} & 2^{2} & 3^{2} & 4^{2} \\ 2^{2} & 3^{2} & 4^{2} & 5^{2} \\ 3^{2} & 4^{2} & 5^{2} & 6^{2} \\ 4^{2} & 5^{2} & 6^{2} & 7^{2} \end{matrix} |$

Evaluate :

$| \begin{matrix} 1 & a & b c \\ 1 & b & c a \\ 1 & c & a b \end{matrix} |$

Evaluate the following:

$| \begin{matrix} x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x \end{matrix} |$

Using determinants show that the following points are collinear:

(3, −2), (8, 8) and (5, 2)

x + 2y = 5
3x + 6y = 15

2x + y − 2z = 4
x − 2y + z = − 2
5x − 5y + z = − 2

Solve each of the following system of homogeneous linear equations.
x + y − 2z = 0
2x + y − 3z = 0
5x + 4y − 9z = 0

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.

State whether the matrix
$[\begin{matrix} 2 & 3 \\ 6 & 4 \end{matrix}]$ is singular or non-singular.

Find the value of the determinant
$[\begin{matrix} 4200 & 4201 \\ 4205 & 4203 \end{matrix}]$

If $A = [a_{i j}]$ is a 3 × 3 diagonal matrix such that a₁₁ = 1, a₂₂ = 2 a₃₃ = 3, then find |A|.

If I₃ denotes identity matrix of order 3 × 3, write the value of its determinant.

Write the value of $| \begin{matrix} a + i b & c + i d \\ - c + i d & a - i b \end{matrix} | .$

Evaluate: $| \begin{matrix} \cos 15^{\circ} & \sin 15^{\circ} \\ \sin 75^{\circ} & \cos 75^{\circ} \end{matrix} |$

If $| \begin{matrix} 2 x & x + 3 \\ 2 (x + 1) & x + 1 \end{matrix} | = | \begin{matrix} 1 & 5 \\ 3 & 3 \end{matrix} |$ , then write the value of x.

Using the factor theorem it is found that a + b, b + c and c + a are three factors of the determinant

| \begin{matrix} - 2 a & a + b & a + c \\ b + a & - 2 b & b + c \\ c + a & c + b & - 2 c \end{matrix} |

The other factor in the value of the determinant is

The value of $| \begin{matrix} 5^{2} & 5^{3} & 5^{4} \\ 5^{3} & 5^{4} & 5^{5} \\ 5^{4} & 5^{5} & 5^{6} \end{matrix} |$

If x, y, z are different from zero and $| \begin{matrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{matrix} | = 0$ , then the value of x⁻¹ + y⁻¹ + z⁻¹ is

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 = 3
2x − y + z = − 1
2x + y − 3z = − 9

Show that the following systems of linear equations is consistent and also find their solutions:
x + y + z = 6
x + 2y + 3z = 14
x + 4y + 7z = 30

A = [\begin{matrix} 1 & - 2 & 0 \\ 2 & 1 & 3 \\ 0 & - 2 & 1 \end{matrix}] and B = [\begin{matrix} 7 & 2 & - 6 \\ - 2 & 1 & - 3 \\ - 4 & 2 & 5 \end{matrix}]

, find AB. Hence, solve the system of equations: x − 2y = 10, 2x + y + 3z = 8 and −2y + z = 7

The prices of three commodities P, Q and R are Rs x, y and z per unit respectively. A purchases 4 units of R and sells 3 units of P and 5 units of Q. B purchases 3 units of Q and sells 2 units of P and 1 unit of R. Cpurchases 1 unit of P and sells 4 units of Q and 6 units of R. In the process A, B and C earn Rs 6000, Rs 5000 and Rs 13000 respectively. If selling the units is positive earning and buying the units is negative earnings, find the price per unit of three commodities by using matrix method.

A = [\begin{matrix} 2 & 4 \\ 4 & 3 \end{matrix}], X = (\binom{n}{1}), B = (\binom{8}{11})

and AX = B, then find n.

Show that $| \begin{matrix} y + z & x & y \\ z + x & z & x \\ x + y & y & z \end{matrix} | = (x + y + z) {(x - z)}^{2}$

Write the value of $| \begin{matrix} a - b & b - c & c - a \\ b - c & c - a & a - b \\ c - a & a - b & b - c \end{matrix} |$

If A = $[\begin{matrix} 1 & - 1 & 2 \\ 3 & 0 & - 2 \\ 1 & 0 & 3 \end{matrix}]$ , verify that A(adj A) = (adj A)A

If $| \begin{matrix} 2 x & 5 \\ 8 & x \end{matrix} | = | \begin{matrix} 6 & 5 \\ 8 & 3 \end{matrix} |$ , then find x

If $| \begin{matrix} 2 x & 5 \\ 8 & x \end{matrix} | = | \begin{matrix} 6 & - 2 \\ 7 & 3 \end{matrix} |$ , then value of x is ______.

The value of λ, such that the following system of equations has no solution, is

$2 x - y - 2 z = - 5$

$x - 2 y + z = 2$

$x + y + λ z = 3$

What is the nature of the given system of equations

$\begin{array}{l} x + 2 y = 2 \\ 2 x + 3 y = 3 \end{array}$

Notifications

English हिंदी मराठी

Login

Create free account

Course

वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ सी. बी. एस. ई.

Change mode
Log out

Select a course

Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.