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Yogita Ingle 4 years, 3 months ago
Expanding along R1
x(x2−12)−3(2x−14)+7(12−7x)=0
⇒x3−12x−6x+42+84−49x=0
⇒x3−67x+126=0 ………………i
Here 126×1=9×2×7126×1=9×2×7
For x=2, 23−67×2+126=134−134=0
Hence x=2 is a root.
For x=7,63−67×7+126=469−169=0
Hence x=7 is also a root.
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Meghna Thapar 4 years, 3 months ago
The closure property means that a set is closed for some mathematical operation. That is, a set is closed with respect to that operation if the operation can always be completed with elements in the set. Thus, a set either has or lacks closure with respect to a given operation. A set is closed under an operation if performance of that operation on members of the set always produces a member of that set. For example, the positive integers are closed under addition, but not under subtraction: is not a positive integer even though both 1 and 2 are positive integers.
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Class 12
Chapter 4: Determinants
Determinant
Every square matrix A is associated with a number, called its determinant and it is denoted by det (A) or |A| .
Only square matrices have determinants. The matrices which are not square do not have determinants
Posted by Antony Jeslin 4 years, 3 months ago
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Gaurav Seth 4 years, 3 months ago
Consider the composition table :
LCM | 1 | 2 | 3 | 4 | 5 |
1 | 1 | 2 | 3 | 4 | 5 |
2 | 2 | 2 | 6 | 4 | 10 |
3 | 3 | 5 | 3 | 12 | 15 |
4 | 4 | 4 | 12 | 4 | 20 |
5 | 5 | 10 | 15 | 20 | 5 |
In the given composition table, all the elements are not in the set {1, 2, 3, 4, 5}.
If we consider a = 2 and b = 3, a * b = LCM of a and b = 6 ∉ {1, 2, 3, 4, 5}.
Thus, * is not a binary operation on {1, 2, 3, 4, 5}.
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