Two matrices are said to be equal if :
Both the matrices are of the same order i.e., they have the same number of rows and columns A_{m × n} = B_{m × n} .
Problem 1 :
Solution :
Equation (2), multiplying (2) on each sides.
2r + 8s = -4 --- (3)
Subtracting the equation (1) and (3).
(2r - 3s - 2r - 8s) = 4 + 4
-11s = 8
s = -8/11
s = -8/11 substitute the equation (1).
2r - 3(-8/11) = 4
2r + 24/11 = 4
2r = 4 - (24/11)
2r = (44 - 24)/11
2r = 20/11
Dividing 2 on each sides.
r = 1/2 × 20/11
r = 10/11
So, the values of r and s is -8/11 and 10/11.
Problem 2 :
Solve each matrix equation or system of equations by using inverse matrices.
Solution :
So, the values of a and b is 1.5 and -4.
Problem 3 :
Solve each equation.
Solution :
Equating the equation :
2y - x = 3 ---- (1)
x = 4y - 1
x - 4y = -1--- (2)
Solving equation (1) and (2)
(2y - x) + (x - 4y) = 3 - 1
2y - x + x - 4y = 2
-2y = 2
y = -2/2
y = -1
y = -1 substitute the equation (2)
x - 4(-1) = -1
x + 4 = -1
x = -1 - 4
x = -5
So, the values of x and y is -1 and -5.
Problem 4 :
Solution :
7x = 5 + 2y
7x - 2y = 5 --- (1)
x + y = 11 --- (2)
Solving equation (1) and (2)
(7x - 2y) + (x + y) = 5 + 11
8x - y = 16
8x = 16 + y
x = (16 + y)/8 --- (3)
x = (16 + y)/8 substitute the equation (2).
(16 + y)/8 + y = 11
Multiplying 8 on each sides.
16 + y + 8y = 88
16 + 9y = 88
9y = 88 - 16
9y = 72
y = 72/9
y = 8
x = 8 substitute the equation (2).
x + 8 = 11
x = 11 - 8
x = 3
So, the values of x and y is 3 and 8.
Problem 5 :
Solution :
Equating the corresponding elements, we get
2x = -16
x = -16/2
x = -8
y + 1 = -7
y = -7 - 1
y = -8
z - 8 = -2
z = -2 + 8
z = 6
So, the values of x, y and z is -8, -8 and 6.
Problem 6 :
Solution :
Problem 7 :
Solution :
4|(-3 × 3) - (2 × 1)| - x|(-x × 3) - (-6 × 1)| - 2|(-x × 2) - (-6 × (-3))| = -3
4(-9 - 2) - x(-3x + 6) - 2(-2x - 18) = -3
4(-11) + 3x^{2} - 6x + 4x + 36 = -3
-44 + 3x^{2} - 2x + 36 + 3 = 0
3x^{2} - 2x - 5 = 0
3x^{2} - 5x + 3x - 5 = 0
x(3x - 5) + 1(3x - 5) = 0
(x + 1) (3x - 5) = 0
x + 1 = 0 and 3x - 5 = 0
x = -1 and 3x = 5
x = 5/3
So, the value of x is -1 and 5/3.
Problem 8 :
Solution :
Equating the corresponding elements, we get
x^{2} + 1 = 5
x^{2} = 5 - 1
x^{2} = 4
x = ±2
5 - y = x Put x = 2 5 - y = 2 -y = 2 - 5 -y = -3 y = 3 |
Put x = -2 5 - y = -2 -y = -2 - 5 -y = -7 y = 7 |
So, the values of x and y is ±2 and 3 and 7.
Problem 9 :
Solution :
Equating the corresponding elements, we get
3x - 5 = 10
3x = 10 + 5
3x = 15
x = 15/3
x = 5
x + y = 8
Put x = 5
5 + y = 8
y = 8 - 5
y = 3
9z = 3x + y
Put x = 5 and y = 3
9z = 3(5) + 3
9z = 15 + 3
9z = 18
z = 18/9
z = 2
So, the values of x, y and z is 5, 3 and 2.
Dec 08, 23 08:03 AM
Dec 08, 23 07:32 AM
Dec 08, 23 07:10 AM