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Let f: W → W be defined as f(n) = n − 1, if is odd and f(n) = n + 1, if n is even. Show that f is invertible. Find the inverse of f. Here, W is the set of all whole numbers.
Concept: undefined >> undefined
If f: R → R is defined by f(x) = x2 − 3x + 2, find f(f(x)).
Concept: undefined >> undefined
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Let A be a nonsingular square matrix of order 3 × 3. Then |adj A| is equal to ______.
Concept: undefined >> undefined
Examine the consistency of the system of equations.
x + 2y = 2
2x + 3y = 3
Concept: undefined >> undefined
Examine the consistency of the system of equations.
2x − y = 5
x + y = 4
Concept: undefined >> undefined
Examine the consistency of the system of equations.
x + 3y = 5
2x + 6y = 8
Concept: undefined >> undefined
Examine the consistency of the system of equations.
x + y + z = 1
2x + 3y + 2z = 2
ax + ay + 2az = 4
Concept: undefined >> undefined
Examine the consistency of the system of equations.
3x − y − 2z = 2
2y − z = −1
3x − 5y = 3
Concept: undefined >> undefined
Examine the consistency of the system of equations.
5x − y + 4z = 5
2x + 3y + 5z = 2
5x − 2y + 6z = −1
Concept: undefined >> undefined
Solve the system of linear equations using the matrix method.
5x + 2y = 4
7x + 3y = 5
Concept: undefined >> undefined
Solve the system of linear equations using the matrix method.
2x – y = –2
3x + 4y = 3
Concept: undefined >> undefined
Solve the system of linear equations using the matrix method.
4x – 3y = 3
3x – 5y = 7
Concept: undefined >> undefined
Solve the system of linear equations using the matrix method.
5x + 2y = 3
3x + 2y = 5
Concept: undefined >> undefined
Solve the system of linear equations using the matrix method.
2x + y + z = 1
x – 2y – z = `3/2`
3y – 5z = 9
Concept: undefined >> undefined
Solve the system of linear equations using the matrix method.
x − y + z = 4
2x + y − 3z = 0
x + y + z = 2
Concept: undefined >> undefined
Solve the system of linear equations using the matrix method.
2x + 3y + 3z = 5
x − 2y + z = −4
3x − y − 2z = 3
Concept: undefined >> undefined
Solve the system of linear equations using the matrix method.
x − y + 2z = 7
3x + 4y − 5z = −5
2x − y + 3z = 12
Concept: undefined >> undefined
If A = `[(2,-3,5),(3,2,-4),(1,1,-2)]` find A−1. Using A−1 solve the system of equations:
2x – 3y + 5z = 11
3x + 2y – 4z = –5
x + y – 2z = –3
Concept: undefined >> undefined
The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs. 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs. 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs. 70. Find the cost of each item per kg by matrix method.
Concept: undefined >> undefined
Solve the system of the following equations:
`2/x+3/y+10/z = 4`
`4/x-6/y + 5/z = 1`
`6/x + 9/y - 20/x = 2`
Concept: undefined >> undefined
