Answer:
a) -4
b) 1
c) 1
Step-by-step explanation:
a) The matrix A is given by:
to find the eigenvalues of the matrix you use the following:
where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:
and by taking the determinant:
and the roots of this polynomial is:
hence, the real eigenvalue of the matrix A is -4.
b) The multiplicity of the eigenvalue is 1.
c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)
Answer:
78 ml of 7% vinegar and 312 ml of 12% vinegar.
Step-by-step explanation:
Let x represent ml of 7% vinegar brand and y represent ml of 12% vinegar brand.
We have been given that chef wants to make 390 milliliters of the dressing. We can represent this information in an equation as:
We are also told that 1st brand 7% vinegar, so amount of vinegar in x ml would be .
The second brand contains 12 vinegar, so amount of vinegar in y ml would be .
We are also told that the chef wants to make 390 milliliters of a dressing that is 11% vinegar. We can represent this information in an equation as:
Upon substituting equation (1) in equation (2), we will get:
Therefore, the chef should use 78 ml of the brand that contains 7% vinegar.
Upon substituting in equation (1), we will get:
Therefore, the chef should use 312 ml of the brand that contains 12% vinegar.
Increasing 50 by x% can be written as:
.................(1)
Decreasing 70 by x % can be represented by the expression:
...........(2)
Now we are given in the question that if we increase 50 by x% and 70 by x%, then the two values are equal.
so equating (1) and (2) , we get
bringing 0.01x to the left side:
taking 50 to the right side, subtracting it from 70
dividing both sides by 0.02
Answer x=2000