Every orthogonal matrix is diagonalizable. O True O False
1 answer:
Answer:
FALSE
Step-by-step explanation:
the correct answer is FALSE
A matrix is said to be orthogonal when it is multiplied by its own transpose then the matrix comes out to be Identity.
the basic condition for a matrix to be diagonalizable is that the matrix should be symmetric.
but an orthogonal matrix is not necessarily symmetric so, the statement is false.
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Answer:
f(8) = -30 is the maximum
Step-by-step explanation:
The equation is that of a parabola in vertex form:
y = a(x -h)^2 +k . . . . . . . . (h, k) is the vertex; 'a' is the scale factor
Comparing this form to the given equation, we have ...
f(x) = -(x -8)^2 -30
- a = -1
- h = 8
- k = -30
That is, the scale factor is -1, and the vertex is (8, -30).
When the scale factor is negative, the graph opens downward and the vertex is a maximum. The maximum value is -30.
