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

1 answer:

3 0

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.

You might be interested in

Mark is planning to run in a 10-km race he will have to run 1 4/5 km uphill, 2 7/10 km downhill, and the rest of the race on lev

777dan777 [17]

Uphill distance = 1 4/5 = 9/5 = 18/10 km Downhill Distance = 2 7/10 = 27/10 km Total Uphill and Downhill = 18/10 + 27/10 = 45/10 = 4.5 km Hence total level ground = Total race km - (Uphill + Downhill) =10 - 4.5 = 5.5 km Hence the answer is 5.5 km.

7 0

3 years ago

Plz help me like plzzzzz

Bingel [31]

Is there a picture of the ramp?

6 0

3 years ago

Read 2 more answers

The area of a rectangle is 56 cm. the length is 2 less than x and the width is 5 less than twice of x. solve for x

Nostrana [21]

Answer:

$x=\frac{9+\sqrt{449}}{4}$

Step-by-step explanation:

The area of a rectangle is:

$A=l\cdot w$

First let's write both the length and the width in terms of x:

$l=x-2$

How we obtained the answer:

The question states the length is "2 less than x". In this case, "less" is a keyword that represents subtraction. Therefore, "2 less than x" is "x-2".

$w=2x-5$

How we obtained the answer:

The question states the width is "5 less than twice of x". First, start by figuring out what "twice of x" is. The keyword is "twice" which represents multiplication. Therefore, "twice of x" can be written as "2x". Then, using the same keyword from before ("less"), "5 less than..." represents "2x-5".

Given:

Area = 56 cm

$l=x-2$

$w=2x-5$

Find:

$A=l\cdot w$

$56=(x-2)(2x-5)$