X − 4y − Z = 11 2x − 5y + 2z = 39 − 3x + 2y + Z = 1 - Mathematics

प्रश्न

x − 4y − z = 11
2x − 5y + 2z = 39
− 3x + 2y + z = 1

उत्तर

Given: x − 4y − z = 11
2x − 5y + 2z = 39
− 3x + 2y + z = 1

$D = | \begin{matrix} 1 & - 4 & - 1 \\ 2 & - 5 & 2 \\ - 3 & 2 & 1 \end{matrix} |$
$= 1 (- 5 - 4) - (- 4) (2 + 6) + (- 1) (4 - 15)$
$= 1 (- 9) - (- 4) (8) + (- 1) (- 11) = 34$
$D_{1} = | \begin{matrix} 11 & - 4 & - 1 \\ 39 & - 5 & 2 \\ 1 & 2 & 1 \end{matrix} |$
$= 11 (- 5 - 4) - (- 4) (39 - 2) + (- 1) (78 + 5)$
$= 11 (- 9) - (- 4) (37) + (- 1) (83) = - 34$
$D_{2} = | \begin{matrix} 1 & 11 & - 1 \\ 2 & 39 & 2 \\ - 3 & 1 & 1 \end{matrix} |$
$= 1 (39 - 2) - 11 (2 + 6) + (- 1) (2 + 117)$
$= 1 (37) - 11 (8) + (- 1) (119) = - 170$
$D_{3} = | \begin{matrix} 1 & - 4 & 11 \\ 2 & - 5 & 39 \\ - 3 & 2 & 1 \end{matrix} |$
$= 1 (- 5 - 78) - (- 4) (2 + 117) + 11 (4 - 15)$
$= 1 (- 83) - (- 4) (119) + 11 (- 11) = 272$
Now,
$x = \frac{D_{1}}{D} = \frac{- 34}{34} = - 1$
$y = \frac{D_{2}}{D} = \frac{- 170}{34} = - 5$
$z = \frac{D_{3}}{D} = \frac{272}{34} = 8$
$∴ x = - 1, y = - 5 and z = 8$

shaalaa.com

Applications of Determinants and Matrices

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 12 Q 11 Q 13

अध्याय 6: Determinants - Exercise 6.4 [पृष्ठ ८४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12

अध्याय 6 Determinants
Exercise 6.4 | Q 12 | पृष्ठ ८४

वीडियो ट्यूटोरियलVIEW ALL [5]

view
वीडियो 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.

5x + 2y = 4

7x + 3y = 5

Solve system of linear equations, using matrix method.

5x + 2y = 3

3x + 2y = 5

Evaluate the following determinant:

$| \begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix} |$

Evaluate the following determinant:

$| \begin{matrix} a + i b & c + i d \\ - c + i d & a - i b \end{matrix} |$

Find the value of x, if

$| \begin{matrix} x + 1 & x - 1 \\ x - 3 & x + 2 \end{matrix} | = | \begin{matrix} 4 & - 1 \\ 1 & 3 \end{matrix} |$

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

$| \begin{matrix} 2 & 3 & 7 \\ 13 & 17 & 5 \\ 15 & 20 & 12 \end{matrix} |$

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:

$| \begin{matrix} a & b & c \\ a + 2 x & b + 2 y & c + 2 z \\ x & y & z \end{matrix} |$

Evaluate :

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

Evaluate the following:

$| \begin{matrix} 0 & x y^{2} & x z^{2} \\ x^{2} y & 0 & y z^{2} \\ x^{2} z & z y^{2} & 0 \end{matrix} |$

Prove that

$| \begin{matrix} \frac{a^{2} + b^{2}}{c} & c & c \\ a & \frac{b^{2} + c^{2}}{a} & a \\ b & b & \frac{c^{2} + a^{2}}{b} \end{matrix} | = 4 a b c$

Using properties of determinants prove that

$| \begin{matrix} x + 4 & 2 x & 2 x \\ 2 x & x + 4 & 2 x \\ 2 x & 2 x & x + 4 \end{matrix} | = (5 x + 4) {(4 - x)}^{2}$

Prove the following identity:

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

Find the area of the triangle with vertice at the point:

(−1, −8), (−2, −3) and (3, 2)

2x − y = 1
7x − 2y = −7

Prove that :

| \begin{matrix} 1 & b + c & b^{2} + c^{2} \\ 1 & c + a & c^{2} + a^{2} \\ 1 & a + b & a^{2} + b^{2} \end{matrix} | = (a - b) (b - c) (c - a)

Prove that :

| \begin{matrix} 1 & a^{2} + b c & a^{3} \\ 1 & b^{2} + c a & b^{3} \\ 1 & c^{2} + a b & c^{3} \end{matrix} | = - (a - b) (b - c) (c - a) (a^{2} + b^{2} + c^{2})

6x + y − 3z = 5
x + 3y − 2z = 5
2x + y + 4z = 8

x + y + z + 1 = 0
ax + by + cz + d = 0
a²x + b²y + x²z + d² = 0

3x + y = 5
− 6x − 2y = 9

If $A = [\begin{matrix} 1 & 2 \\ 3 & - 1 \end{matrix}] and B = [\begin{matrix} 1 & 0 \\ - 1 & 0 \end{matrix}]$ , find |AB|.

If $A = [\begin{matrix} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{matrix}]$ . Write the cofactor of the element a₃₂.

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.

If $| \begin{matrix} 3 x & 7 \\ - 2 & 4 \end{matrix} | = | \begin{matrix} 8 & 7 \\ 6 & 4 \end{matrix} |$ , find the value of x.

If a > 0 and discriminant of ax² + 2bx + c is negative, then
$∆ = | \begin{matrix} a & b & a x + b \\ b & c & b x + c \\ a x + b & b x + c & 0 \end{matrix} | i s$

There are two values of a which makes the determinant $∆ = | \begin{matrix} 1 & - 2 & 5 \\ 2 & a & - 1 \\ 0 & 4 & 2 a \end{matrix} |$ equal to 86. The sum of these two values is

Solve the following system of equations by matrix method:
3x + y = 19
3x − y = 23

Solve the following system of equations by matrix method:
x + y + z = 3
2x − y + z = − 1
2x + y − 3z = − 9

2x − y + 2z = 0
5x + 3y − z = 0
x + 5y − 5z = 0

3x − y + 2z = 0
4x + 3y + 3z = 0
5x + 7y + 4z = 0

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

On her birthday Seema decided to donate some money to children of an orphanage home. If there were 8 children less, everyone would have got ₹ 10 more. However, if there were 16 children more, everyone would have got ₹ 10 less. Using the matrix method, find the number of children and the amount distributed by Seema. What values are reflected by Seema’s decision?

System of equations x + y = 2, 2x + 2y = 3 has ______

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

If the system of equations x + ky - z = 0, 3x - ky - z = 0 & x - 3y + z = 0 has non-zero solution, then k is equal to ____________.

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

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

$x - 2 y + z = 2$

$x + y + λ z = 3$

In system of equations, if inverse of matrix of coefficients A is multiplied by right side constant B vector then resultant will be?

The number of real value of 'x satisfying $| \begin{matrix} x & 3 x + 2 & 2 x - 1 \\ 2 x - 1 & 4 x & 3 x + 1 \\ 7 x - 2 & 17 x + 6 & 12 x - 1 \end{matrix} |$ = 0 is

The number of real values λ, such that the system of linear equations 2x – 3y + 5z = 9, x + 3y – z = –18 and 3x – y + (λ² – |λ|z) = 16 has no solution, is ______.

X − 4y − Z = 11 2x − 5y + 2z = 39 − 3x + 2y + Z = 1 - Mathematics

Advertisements

Advertisements

प्रश्न

उत्तर

APPEARS IN

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Select a course

X − 4y − Z = 11 2x − 5y + 2z = 39 − 3x + 2y + Z = 1 - Mathematics

Advertisements

Advertisements

प्रश्न

उत्तरShow Solution

APPEARS IN

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Select a course

उत्तर