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EleoNora [17]
3 years ago
11

Given the following matrices A and B, find an invertible matrix U such that UA = B:

Mathematics
1 answer:
Naddik [55]3 years ago
3 0

<span>A and B must be invertible, we have UA=B, since A is invertible.  A^-1 exists, by multiplying with A^-1, we have UA A^-1 =B A^-1. But AA^-1 = I (identity matrix) and XI=X, for all matrix X, we find UI= B A^-1, and U= B A^-1.</span>

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I need help with this. Please include explanation.
GrogVix [38]

Step-by-step explanation:

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2 years ago
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I NEED HELP WITH THIS PLEASE !!! AND EXPLAINED PLEASE!
Ksenya-84 [330]

Answer:

Step-by-step explanation:

Find the vertex and intercepts of y = 3x2 + x – 2 and graph; remember to label the vertex and the axis of symmetry.

This is the same quadratic as in the last example. I already found the vertex when I worked the problem above. This time, I also need to find the intercepts before I do my graph. To find the y-intercept, I set x equal to zero and solve:

y = 3(0)2 + (0) – 2

= 0 + 0 – 2 = –2

Then the y-intercept is the point (0, –2). To find the x-intercept, I set y equal to zero, and solve:

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Then the x-intercepts are at the points (–1, 0) and ( 2/3, 0).

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The complete answer is a listing of the vertex, the axis of symmetry, and all three intercepts, along with a nice neat graph:

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graph of y = 3x^2 + x - 2 with vertex and intercepts marked.

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y = (0)2 – (0) – 12 = 0 – 0 – 12 = –12

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0 = x2 – x – 12

0 = (x – 4)(x + 3)

x = 4 or x = –3

To find the vertex, I look at the coefficients: a = 1 and b = –1. Plugging into the formula, I get:

h = –(–1)/2(1) = 1/2 = 0.5

To find k, I plug h = 1/2 in for x inside y = x2 – x – 12, and simplify:

k = (1/2)2 – (1/2) – 12 = 1/4 – 1/2 – 12 = –12.25

Once I have the vertex, it's easy to write down the axis of symmetry: x = 0.5. Now I'll find some additional plot points, to fill in the graph:

T-chart

For my own convenience, I picked x-values that were centered around the x-coordinate of the vertex. Now I can plot the parabola: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

graph of y = x^2 - x - 12

The vertex is at the point (0.5, –12.25),

the axis of symmetry is the line x = 0.5,

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Sorry I don’t know
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AleksandrR [38]

Answer:

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Step-by-step explanation:

For this case we know that the french fries cost $0.50 and we want to have a margin of 75% on the fries. So we can use the following proportional rule:

\frac{0.5}{100} = \frac{x}{175}

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