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lbvjy [14]
3 years ago
5

Suppose that A is nonsingular. Prove that its inverse A-1 is unique. [Hint: Show that if there exists two matrices, B and C, suc

h that BA = I and AC −=I, then necessarily B =C.]
Mathematics
1 answer:
Bogdan [553]3 years ago
4 0

Answer with Step-by-step explanation:

Let A is non-singular

\mid A\mid\neq 0

We have to prove that A^{-1} is unique.

Suppose B and C are inverse of A such that

BA=I and AC=I

By using property AA^{-1}=A^{-1}A=I

C=C

(BA)C=B(AC)

I\cdot C=B\cdot I

C=B

Hence, the inverse of A is unique.

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|-5c+5|=40 solve for c
GrogVix [38]

Answer:

C=9 or c=-7

Step-by-step explanation:

|-5c+5|=40

-5c+5=-40 or - 5c+5=40

-5c=-40-5. - 5c=40-5

-5c=-45. - 5c=35

C=9. C=-7

5 0
3 years ago
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The base of an isosceles triangle is a fourth as long as the two equal sides. write the perimeter of the triangle as a function
jeka57 [31]
Set the length of the base as x, the two equal sides are then 4x each, so the perimeter is x+4x+4x=9x
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Which of the following systems of inequalities has solutions represented by the graph shown below?
Digiron [165]

Answer:

y ≤ 1/2x - 1

y ≤ -2x + 4

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write an equation in slop-intercept form for a line that is perpendicular to the line y= -5x-3 and has a y-intercept of 6.
jenyasd209 [6]

Answer:

The equation of the line would be y = 1/5x + 6

Step-by-step explanation:

First, to find the slope of a perpendicular line, you need to find the opposite and reciprocal of the original slope. Since the original is -5, we first change the sign (which makes it just 5). Now we take that 5 and flip it to get 1/5.

Now that we have the slope as 1/5, we can use that and the intercept in slope-intercept form to get the equation.

y = mx + b

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3 years ago
Rewrite the equation by completing the square.<br> 4x2 + 28x + 49 = 0<br> (x+) =
Vlada [557]

Answer: x = - 3.5

Step-by-step explanation:

Rewrite the equation by completing the square.

4x2 + 28x + 49 = 0

Completing the square method :

Divide through by the Coefficient of x^2

x^2 + 7x + (49/4) = 0

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Move c to the right side of the equation

x^2 + 7x = - 49/4

Complete the square on the left hand side by squaring its half of the x term

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Add the output to both sides of the equation

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(x + 7/2)^2 = 0

Square root of both sides

x + 7/2 = 0

x = - 7/2

x = - 3.5

4 0
3 years ago
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