Let A be a 3×2 matrix, L its left inverse, and R its right inverse. L and R are then matrices such that LA = I₂ (the 2×2 identity matrix) and AR = I₃ (the 3×3 identity matrix). Clearly L must be 2×3 and R must be 3×2 in order for the matrix products to be defined.
To find L and R, we start by introducing a square matrix on the the left sides of either equation above. In particular, we uniformly multiply both sides by the transpose of A, then solve for the inverse.
For the left inverse, we have
[tex]LA=I[/tex]
[tex](LA)A^\top = IA^\top[/tex]
[tex]L\left(AA^\top\right) = A^\top[/tex]
[tex]\left(L\left(AA^\top\right)\right)\left(AA^\top\right)^{-1} = A^\top \left(AA^\top\right)^{-1}[/tex]
[tex]L\left(\left(AA^\top\right)\left(AA^\top\right)^{-1}\right) = A^\top \left(AA^\top\right)^{-1}[/tex]
[tex]LI = A^\top \left(AA^\top\right)^{-1}[/tex]
[tex]L = A^\top \left(AA^\top\right)^{-1}[/tex]
We do the same thing for the right inverse, but take care with how we multiply both sides of AR = I₃.
[tex]AR=I[/tex]
[tex]A^\top(AR)=A^\top I[/tex]
[tex]\left(A^\top A\right)R = A^\top[/tex]
[tex]\left(A^\top A\right)^{-1} \left(\left(A^\top A\right)R\right) = \left(A^\top A\right)^{-1} A^\top[/tex]
[tex]\left(\left(A^\top A\right)^{-1} \left(A^\top A\right)\right) R = \left(A^\top A\right)^{-1} A^\top[/tex]
[tex]IR = \left(A^\top A\right)^{-1} A^\top[/tex]
[tex]R = \left(A^\top A\right)^{-1} A^\top[/tex]
The final grade on your math exam was determined by the function f(x) = 100 − 2x. Which statements are correct?
A) 100 is the maximum grade.
B) y equals your final grade.
C) This is an exponential function.
D) 2 is what each question is worth.
E) x is the number of correct problems.
Answer:
A. True
B. True
C. False
D. True
E. False
Step-by-step explanation:
A. True, you cannot get higher than 100 on this test , as you cannot get a negative amount of questions wrongs
B. True, as y = f(x)
C. False, as there is no exponents
D. True, as if x=1, you lose 2 points
E. False, as x is the number of wrong problems
PLEASE HELP ME WITH THESE MATH PROBLEMS!! DUE TONIGHT!!
Answer:
a) 20.9ft b)148.5ft c)98.2ft d)50.3
Step-by-step explanation:
for a, b and c you can use SOHCAHTOA
a) sin(8)=height/150 so height=150sin(8)
b)cos(8)=distance/150 rearrange the same way
c)use SOHCAHTOA but with the value you got from a ad the 12 degree angle
d) subtract the value found in c from the value found in a
10 x 9= what is it help
Answer:
10
[tex]10 \times 9 \\ 90[/tex]
Answer:
90 :)
Step-by-step explanation:
10 x 9 = 90
= 90 is correct answer
(Hope this helps can I pls have brainlist (crown)☺️)
W to the 3rd power over W to the -2 power
Answer:
[tex]w^{5}[/tex], w to the power of 5
Step-by-step explanation:
[tex]\frac{w^3}{w^-2}[/tex]
When dividing indices with the same base number, you can subtract the powers: 3 - (-2) = 5. Therefore the answer is [tex]w^{5}[/tex]
Hope this helps!
A formula is given with the value of all but one of the variables in the formula. Find the value of the variable not given.
P=2L + 2W; L= 4, W = 8
Answer:
P = 24
Step-by-step explanation:
P = 2L + 2W ( substitute L = 4, W = 8 into the formula )
P = 2(4) + 2(8) = 8 + 16 = 24
Answer :
Step-by-step explanation:
P=2(4)+2(8)
P=8+16
P= 24
Miko filled two tanks with water. The ratio of the amount of water in Tank A to Tank B is 3 : 2. The total amount of water in both tanks is 210 ℓ. How much water must Miko pour from Tank A into Tank B so that both tanks have the same amount of water?
Step-by-step explanation:
answer is in the above picture
Does anyone know this ??
bbbbbbbbbbbbbbbbbbbbbbbbbbbvbbbbbbbbbbb
share £165 in the ratio 2:3
Select all statements that are true about the triangles.
Figure ABCD with diagonal BC, sides AB and DC are congruent, angle A is congruent to angle D and sides AC and DB are congruent.
Group of answer choices
Triangles ABC and BCD are congruent by the Angle-Side-Angle Triangle Congruence Theorem.
Triangles ABC and DCB are congruent by the Angle-Angle Triangle Congruence Theorem.
Triangles ABC and DCB are congruent by the Side-Side-Side Triangle Congruence Theorem.
Triangles ABC and DCB are congruent by the Side-Angle-Side Triangle Congruence Theorem.
Triangles ABC and BCD are congruent by the Side-Side-Side Triangle Congruence Theorem.
There is not enough information to determine if the triangles are congruent
Answer:
Triangle ABC and BCD are congruent by the side side side triangle congruence theorem
y= -8/9 (x+1)+6
convert to standard form
Answer:
mm
kl l
Step-by-step explanation:
Petro's family went out to eat. The bill for the food was 36.25. The restaurant tax was 3.37 and Petro left a tip for 5.75. What is the best estimate for how much the meal cost altogether?
Answer:
45.37
Step-by-step explanation:Based on the given conditions, formulate:
5.75
+
36.25
+
3.37
Calculate the sum or difference:
42
+
3.37
Calculate the sum or difference:
45.37
get the result:
45.37
A group of 15 people are ordering pizza each person wants 2 slices and each pizza has 3 slices how many pizzas should they order
Answer:
Step-by-step explanation:
15*2=30
30/2=10
10 pizzas will evenly divide between 15 ppl and give each 2 slices with no extras.
Total number of pizzas will they order will be 10.
What are mathematics operations?
A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
Here, it is given that :
A group of 15 people are ordering pizza each person wants 2 slices and each pizza has 3 slices.
Now, 15 person will eat = 15 x 2 = 30 slices of pizza
To Find the number of pizza divide total slice of pizza people wanted with slice per pizza :
number of pizza = 30/3 = 10 pizza.
Therefore, total number of pizzas will they order will be 10.
Read more about mathematics operations at:
https://brainly.com/question/17869111
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Evaluate. (4/5)^3this is a fraction, and an exponent, not 4 divided by 5, please get answer in quickly.
Answer:
[tex]\frac{64}{125}[/tex]
Step-by-step explanation:
[tex]\frac{4}{5} ^{3}[/tex]
To solve this you would cube the numerator and then the denominator:
4³ = 645³ = 125The answer is [tex]\frac{64}{125}[/tex]
Hope this helps!
100 IF U GET THIS RIGHT!
Answer:
Eq
● y = mx + c
m = slope
c = intercept
y = 2/9 x + (-2)
slope m=2/9
put a factor back into the square root.
[tex]3 \sqrt{2a}[/tex]
Answer:
sqrt(18a)
Step-by-step explanation:
3^2=9
2*9=18
sqrt(18a)
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The factor that can be put back into the square root is 9.
√(2 x 9 x a) = √(18a) = 3√(2a)
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
3√(2a)
A factor that can be put back into the square root is 9.
√(2 x 9 x a) = √(18a) = 3√(2a)
3² = 9
Thus,
The factor that can be put back into the square root is 9.
√(2 x 9 x a) = √(18a) = 3√(2a)
Learn more about expressions here:
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The vertex of a parabola is (-2,6), and its focus is (-5,6).
What is the standard form of the parabola?
Enter your answer by filling in the boxes.
The equation of the parabola is:
(y - 6)² = -12(x +2)
Parabola is the locus of a point such that its distance from a fixed point (called the focus) and a given line (called the directrix) is always the same.
The equation of a parabola is given by:
(y - k)² = 4p(x - h)
Where (h, k) is the vertex, (h + p, k) is the focus
Given the vertex of a parabola is (-2,6), and its focus is (-5,6).
Hence, k = 6, h = -2;
h + p = -5
-2 + p = -5
p = -3
Hence the equation of the parabola is:
(y - 6)² = -12(x +2)
Find out more at: https://brainly.com/question/21685473
x + 8 less than or equal to 6
How to figure out the absolute value.
Answer:
absolute value is the same number just positive and cha never be negative.
What is a trend line in math.
Answer:
Determining if a set of points exhibits a positive trend, a negative trend, or no trend at all.
A trend line, often referred to as a line of best fit, is a line that is used to represent the behavior of a set of data to determine if there is a certain pattern.
Whats 16 x 32 what does it equal
phân tích đa thức thành nhân tử 8x^2+16xy
Please help! take a pic and put a dot with the drawing tools on ur snipping tool/snip and sketch. Please i cant fail these questions!
Answer:
x > 7/8 and the picture is below.
Step-by-step explanation:
To find the answer, you plug in the values for x. Nothing less than one in the set of given values, works. 1 works, 9/4 works, and 5/2 works. But everything else doesn't. Or, you could simply divide both sides by 2 to get x alone. That makes x>7/8. Meaning 7/8 doesn't work, but anything above it, does. So you could just look for the ones that are greater than 7/8.
GIVING BRAINLIEST!! (ignore the answer i put i accidentally clicked on it) A line passes through the point (-2, 7) and has.a slope of -5.
What is the value of a if the point (a, 2) is also on the line?
Select all of the trips that would take two hours.
a. Drive 60 miles per hour between Raleigh and
Wilmington, which are 120 miles apart
b. Walk 3 miles per hour to school, which is ½ mile
away
c. Take a train going 70 miles per hour from Hershey to
Philadelphia, which are 140 miles apart
Answer:
A and C
Step-by-step explanation:
ive seen this question before
║3x²+x+5║= 5x²- 3x+ 7
Is this what you needed ?
what is the point in the middle of a circle called
Answer:
Step-by-step explanation:
Center: The center of a circle is defined as the point in the middle of the circle. The points that make up the curve that is the circle are all equidistant from the center point.
Answer:
Center of the circle.
Step-by-step explanation:
Please Pleaseee help...will make the brainliest
Answer:
A and F.
Explaination:
Team math Minds have a score of - 200 They answered five 30-point questions correctly. What is their new score?
Please help me
20 points
Answer:
1). Simplify the expression.
Exact Form:
( [tex]\frac{37}{25}[/tex] )
Decimal Form:
1.48
Mixed Number Form:
( [tex]1\frac{12}{25}[/tex] )
2). Simplify the expression.
91.46
3). Simplify the expression.
Exact Form:
[tex]\frac{17}{24}[/tex]
Decimal Form:
0.7083 ( bar notation)
4). Simplify the expression.
81.49
how long is the Yangtze river
Answer:
3,915 mi
Step-by-step explanation:
