Suppose A is n x n matrix and the equation Ax = 0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to In. By Theorem 7, this shows that A must be Invertible.)Theorem 7: An n x n matrix A is invertible if and only if A is row equivalent to In, and in this case, any sequence of elementary row operations that reduces A to In also transfrms In into A-1.

Answers

Answer 1

Answer:

Answer:

Remember, a homogeneous system always is consistent. Then we can reason with the rank of the matrix.

If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.

Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.

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John bought an odd shaped lot that was 100 feet deep, but the front footage was 160 feet and the length of the back side of the lot was 80 feet what is the square footage of his lot?

Answers

Answer:

12000 $ft^(2)$

Step-by-step explanation:

The lot has the shape of a trapezoid. This means that the area can be find using the formula:

$Area= ((B_(1)+B_(2))/(2))h$

Where $B_(1)$ and $B_(2)$ are the two paralle sides (in this case the front side of 160 feet and, the back side of 80) and, h is the height (the deep of 100 feet). So :

$Area= ((160+80)/(2))*100$

$Area= 12000$ square feet.

This lot has the shape of a trapezoid. Regard the 2 different lengths as 160' and 80' and the width 100'

Applying the formula for the area of a trapezoid:

80' + 160'

A = ----------------- * 100' = 24000 ft^3

What is the area of the parallelogram?A.
48 square centimeters

B.
28 square centimeters

C.
12 square centimeters

D.
24 square centimeters

Answers

The area of the parallelogram would be A) 48 Square centimeters because when you are finding the area of parallelogram then you do B*H so the base in this parallelogram is 8 and the height in this parallelogram is 4 and so then you multiply 8 and 4 so 8*4=48...so the answer would be A) 48 Square Centimeters....hope it helped

Use the Special Right Triangle to evaluate sin 60°, cos 60° and tan 60°. Your answers should be exact (not a decimal).A. sin 60 = 1/2, cos 60 = √3/2, tan 60 = √3/3
B. sin 60 = √2/2, cos 60 = √2/2, tan 60 = 1
C. sin 60 = 1, cos 60 = 0, tan 60 = undefined
D. sin 60 = √3/2, cos 60 = 1/2, tan 60 = √3

Answers

sin(60) = ¹/₂√3
cos(60) = ¹/₂
tan(60) = √3

The answer is D.

Answer:

The answer is D.

Step-by-step explanation:

Round 8.043 to the nearest hundredth

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Rounding to the nearest hundredth would make the answer be: 8.04. Just move the digits over twice to the right and if the number is 5 or greater(for the number 3), the answer would have been: 8.05. But since it is a 3(lower than 5), then the answer would just be 8.04.
Hope this helps! :-)

It is 8.because you look at the 4 cuz it is in the hundredths place the you look at the 3 if it is 4 or less take it away if it is 5 or more add 1. It's less so take everything away that is behind the decimal

A stereo costs £320. In a sale it is reduced by 25%. What is the sale price?

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$320* (75)/(100) =320 * (25* 3)/(25* 4) =320* (3)/(4) = 80* 4 * (3)/(4) =80* 3 = \boxed {240}$

Find the product -4(3x-5)

Answers

Answer: -12x+20; $x=-(5)/(3)$

Step-by-step explanation:

$-4(3x-5)\n-4(3x)-(-4)5\n-12x-(-20)\n-12x+20\n(-12x)/(-12)=(20)/(-12)\n x=-(20)/(12) =-(5)/(3)$

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