Answer: 3/2
Step-by-step explanation:
K/3 + 4 = 10
K/3 = 10 - 4
K/3 = 6
K = 6x3
K = 18
Answer:
-9 is your answer for b.
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other. Also note the rule that if you have a positive sign & a negative sign next to each other, the resulting sign would be negative:
b + (-17) = -26
b - 17 = -26
Isolate the variable (b). Add 17 to both sides:
b - 17 (+17) = -26 (+17)
b = -26 + 17
Simplify:
b = -26 + 17
b = -9
-9 is your answer for b.
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Remember the rules:
Addition sign + Positive number = Add (Ex: 7 + 7 = 14)
Addition sign + Negative number = Subtract (Ex: 7 + (-7) = 7 - 7 = 0)
Subtraction sign + Positive number = Subtract (Ex: -3 + 4 = 4 - 3 = 1)
Subtraction sign + Subtraction sign = Add (Ex: 5 - (-5) = 5 + 5 = 10)
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Answer:
True, if with distinct you refer with multiplicity 1.
Step-by-step explanation:
The answer is true, assuming that the matrix has as many distinct eigenvalues than the number of rows and columns of the matrix (we can suppose that with distinct you mean that the multiplicity for each eigenvalue is 1).
Lets suppose that the matrix has size n, and let λ1, λ2, λ3, ..., λn be its eigenvalues. Each eigenvalue has an eigenvector vi such that Avi = λivi.
A matrix C whose columns are those eigenvectors v1...v1, will satisfy that the product A*C is the square matrix of length n with columns λ1v1, λ2v2, ..., λnvn. Hence C⁻¹AC = C⁻¹ * (AC) will be a diagonal matrix (because the columns of AC are multiples of the columns of C, which is the inverse of C⁻¹). This shows that C⁻¹AC = C⁻¹ is a diagonal matrix D, then A = CDC⁻1.