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Butoxors [25]
2 years ago
8

g Problem 2. (1.4 points) Suppose A is an n × n matrix, such that A 2 + 3A − 4I = 0 where I and 0 are the n × n identity and zer

o matrix respectively. What can you say about the invertibility of matrix A?
Mathematics
1 answer:
Pani-rosa [81]2 years ago
6 0

Answer:

The correct answer is A^{-1} = \frac{1}{4} A + \frac{3}{4 }<em> </em>I

Step-by-step explanation:

Since A is an n × n invertible non singular matrix, A^{-1} exists.

Given equation is A^{2} + 3A -4I = O where I and O are the n × n identity and zero matrix respectively.

⇒ A^{2} + 3A -4I = O

⇒ A^{-1} ( A^{2} + 3A -4I ) = A^{-1} × O

⇒ A^{-1} AA + 3 A^{-1}A - 4A^{-1}I = O

⇒ A + 3I - 4A^{-1} = O

⇒ A + 3I = 4 A^{-1}

⇒ A^{-1} = \frac{1}{4} A + \frac{3}{4 }<em> </em>I

Thus the value of  A^{-1} can be given by the above equation.

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Plssss help me, I’ll mark y’all brainliest
My name is Ann [436]

Answer:

1 ray is intersecting point O

Step-by-step explanation:

A ray can be defined as a part of a line that has a fixed starting point but no end point.

AD and EC both go on forever but OB has one endpoint and goes on forever.

3 0
3 years ago
In the figure is a right triangle ABC with AC=10cm and BC=6cm. Determine: 1.5.1 The height AB (hint: Theorem of Pythagoras)
Alexxandr [17]

Answer:

height AB is 8 cm

Step-by-step explanation:

AB= √AC^2- BC^2

= √(10)^2- (6)^2

= √100-36

= √64

= 8

3 0
3 years ago
Question 1 and 2 have the same question help please!!
Hatshy [7]

Answer:

1st Circle

Radius = 9

Diameter = 18

Circumference = 2 × \pi × r = 2 × 3.14 × 9 = 56.52

2nd Circle

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8 0
3 years ago
A subtending arc on a circle with a radius of 4.5 centimeters has an arc length of 8π. The measure of the angle subtended by the
dem82 [27]

Answer: 320°

Step-by-step explanation:

This is a circle geometry.

The arc length of the circle is given to be 8πcm and the radius is 4.5cm.

Now the length of an arc of a circle is

Arc length = πr0°/180° or 2πr0°/360°

To find the angle 0° subtend at the center we equate the arc length with the formula and solve for 0°.Now we go

πr0°/180 = 8π, convert to a simple linear equal and solve for the angle.

πr0° = 8π × 180

0°. = 8π × 180

-----------

π × r

= 8 × 180. 8 × 180

-------- or ---------

9/2. 4.5

= 8 × 180 × 2

------------

9

= 8 × 20 × 2

= 320°

or 8 × 180/4.5

= 1440/4.5

= 320°

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3 years ago
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bazaltina [42]

Answer:

im pretty sure that the answer is a

Step-by-step explanation:


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3 years ago
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