Since the multiplication between two matrices is not commutative, then [tex]\vec A\, \times\,\vec I \ne \vec I \,\times \,\vec A[/tex], regardless of the dimensions of [tex]\vec A[/tex].
Is the product of two matrices commutative?
In linear algebra, we define the product of two matrices as follows:
[tex]\vec C = \vec A \,\times \vec B[/tex], where [tex]\vec A \in \mathbb{R}_{m\times p}[/tex], [tex]\vec B \in \mathbb{R}_{p\times n}[/tex] and [tex]\vec C \in \mathbb{R}_{m \times n}[/tex] (1)
Where each element of the matrix is equal to the following dot product:
[tex]c_{ij} = \left[\begin{array}{cccc}a_{i1}&a_{i2}&\ldots&a_{ip}\end{array}\right]\,\bullet\,\left[\begin{array}{ccc}b_{1j}\\b_{2j}\\\vdots\\b_{pj}\end{array}\right][/tex], where 1 ≤ i ≤ m and 1 ≤ j ≤ n. (2)
Because of (2), we can infer that the product of two matrices, no matter what dimensions each matrix may have, is not commutative because of the nature and characteristics of the definition itself, which implies operating on a row of the former matrix and a column of the latter matrix.
Such "arbitrariness" means that resulting value for [tex]c_{ij}[/tex] will be different if the order between [tex]\vec A[/tex] and [tex]\vec B[/tex] is changed and even the dimensions of [tex]\vec C[/tex] may be different. Therefore, the proposition is false.
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To get to the baseball game, Todd drove 2 hours and 10 minutes, stopped for 15 minutes, then drove 1 hour 15 minutes more to get to the game. If he arrived at 6:10, what time did he leave?
someone please help with the if the domain is restricted between -2
Answer:
The awnser is c.
1.101^3 in normal form
Answer:
The answer is 1,101.
Step-by-step explanation:
1.101 ^ 2 = 11.01
And 1.101 ^ 4 = 11,010.
What is an
equation of the line that passes through the points (8, 5) and (-6, 5):
Answer:
y=8
Step-by-step explanation:
formula of a line equation
y=MX+c
m=Y2-Y1÷X2-X1
m=5-5÷-6-8
m=0÷-14
m=0
substitutionusing (8,5)
8=0(5)+c
8=c
Sarah makes 1/2 pound of caramel popcorn and puts it in a bags that hold 1/8 of a pound which equation can used to find how many bags she can fill
Answer:
1/2 ÷ 1/8 =b
Step-by-step explanation:
the ratio of the angle measures of a triangle are 3:3:4 what angle measures the triangles classification
Step-by-step explanation:
sum of the ratio=3+3+4=10
now,
angle I = 3/10×180=54
angle II= 3/10×180=54
angle III=4/10×180=72
that shows th given triangle is isoceles
como puedo resolver 5 anos en in minuto
Mark the best answer.
1. The grid map shows the location of
some places on a college campus.
What are the coordinates of the
dormitory? (8-1)
Library
Gymnasium
12 Student
Center
5 4 3 2
Dormitory
I.XI
10
2013
Academic
Hall
A (2.1)
B 12)
CK1-2)
D (2.1)
Answer:
it makes sense
Step-by-step explanation:
solve
2. y+0.4=2
what is y?
The answer is,
[tex]y = 1.6[/tex]
Answer:
Y = 1.6
Step-by-step explanation:
Y = 2 - 0.4
Y = 1.6
A boat can travel 77 9/16 nautical miles in 8 1/2 at how many knots is the boat traveling
Divide miles by time:
77 9/16 miles / 8 1/2 hours =
Rewrite as I’m proper fractions:
1241/16 / 17/2
Flip the second fraction over and multiply:
1241/16 x 2/17 = (1241x2)/(16x17) =
2482/272 = 9 1/8 miles per hour
Hi there!
Simplify each terms:
[tex]77\frac{9}{16}*8\frac{1}{2}=77\frac{9}{16}*8\frac{8}{16}[/tex]
Divide each terms:
[tex]77\frac{9}{16}*8\frac{8}{16}=9\frac{2}{16}[/tex]
Simplify terms:
[tex]9\frac{2}{16}=9\frac{1}{8}[/tex]
Final Result:
[tex]9\frac{1}{8}[/tex]
Two points are located on a graph, Point A is (-1, 10), and Point B is (4,3). What is the
distance between Point A and Point B?
A) 8.6
B)13.3
C) 10
D)3
Answer:
10
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRAINLIEST
Is RST = XYZ? If so, name the postulate that applies.
A. Might not be congruent
B. Congruent - SSS
C. Congruent - ASA
D. Congruent - SAS
Answer:
D
Step-by-step explanation:
two sides are congruent and in between is an angle
I need help please.
Answer:
A) c(x)=2x+60
$74
Step-by-step explanation:
A) c(x)=2x+60
$74
Which expression is equivalent to 3x + 6y
A: 3(x + 2y)
B: 3(x + 3y)
C: 9xy
D: 18xy
option a as 3 is outside of bracket it will be multiplied by what is in bracket sot the answer will equivalent to question
The equivalent expression for the given expression is 3(x+2y). Therefore, the correct answer is option A.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is 3x+6y.
Here, the common factor of two terms 3x and 6y is 3
Now, 3(x+2y)
Therefore, option A is the correct answer.
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The hypotenuse of a triangle is one foot more than
twice the length of the shorter leg. The longer leg IS
seven feet longer than the shorter leg. Find the
dimensions of the triangle.
Answer:
y uwu
Step-by-step explanation: i think
Compare the fractions using >, < or=.
9/10 and 78/100
Answer:
9/10 > 78/100
Step-by-step explanation:
We can make 9/10 into 90/100, and since they now have the same denominator (Bottom number in fraction), we can now compare the numerators (Top number in fraction). 90 is greater than 78 so we can say that 9/10 > 78/100 (9/10 is greater than 78/100).
The Roller family spends $134 on 2 adult tickets and 3 youth tickets at an amusement park. The Coaster family
spends $146 on 3 adult tickets and 2 youth tickets at the same park. Find the price of adult and youth tickets,
Answer:
34 adult ticket and 22 youth tickets
Step-by-step explanation:
Let the price of adult be x
Let the price of youth tickets be y
If the Roller family spends $134 on 2 adult tickets and 3 youth tickets at an amusement park, then;
2x+3y = 134 .... 1
Also if the Coaster family spends $146 on 3 adult tickets and 2 youth tickets at the same park then;
3x+2y = 146 ..... 2
Solve simultaneously
2x+3y = 134 .... 1 * 3
3x+2y = 146 ..... 2 * 2
_____________
6x+9y = 402
6x+4y = 292
Subtract
9y-4y = 402-292
5y = 110
y = 110/5
y = 22
Substitute y =22 into 1;
From 1;
2x+3y = 134
2x+3(22) = 134
2x+66 = 134
2x = 134-66
2x = 68
x = 34
Hence there are 34 adult ticket and 22 youth tickets
Convert the angle from radians to degrees.
Answer:
first go to a diffrent site
Step-by-step explanation:
PLEASE HELP MUST BE AT LEAST 5 SENTENCES PLEASE HELP DUE IN 5 MINS
Answer:
I think that Thomas Clarksons motive for publishing this drawing of a slave ship was to inform people what it was like. He wanted to show how crowded it was. Thomas might have wanted to show how people were treated.
( i dunno what else to put but you could talk about how he felt about the slave trade)
need help solving this
Answer:
For this question, subtract 5 on both sides to get [tex]\frac{m}{3}[/tex]=7. Then, multiply 3 on both sides to get m=21.
Answer:
M=21
Hope this helps, and happy valentines day :D
h(t)= 50- t/5
h(35)=
Answer:
h(35) = 43
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
h(t) = 50 - t/5
h(35) is t = 35
Step 2: Evaluate
Substitute in t: h(35) = 50 - 35/5Divide: h(35) = 50 - 7Subtract: h(35) = 43A pair of shoes costs $50. What is the total cost of the shoes after 7.25% tax is added? Round the tax to the nearest cent.
Answer:
Step-by-step explanation:
50(1+7.25/100)
50(107.25/100)
50(1.0725)
53.625
$53.63
Which of these expressions are equivalent to 225 3/2? Select all that apply.
Answer:
C.
Step-by-step explanation:
it could also be written as (sqrt225)^3
C is correct because sqrt225 is equivalent to 225^1/2
using exponent rules, 3 mutiplies to the 1/2 making it 225^3/2
help please...
Which graph represents a proportional relationship?
Answer:
Graph C.
Step-by-step explanation:
The graph which illustrates a proportional relationship is graph c because as the value on the Y-axis increases, the values on the X-axis increases consequently.
A direct proportion implies that the values of the quantities on both sides are increasing at a constant rate. Critically looking at graph c, you will notice or observe that the values both intersect at specific intervals or points on the graph.
): If (6x-3)(6x+3)=ax^2-b, what is the value of a? What is the value of b?
Using traditional methods, it takes 8.1 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 23 students and observed that they had a mean of 8.2 hours with a standard deviation of 1.2. A level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
The value of the test statistic is 0.4.
Step-by-step explanation:
The value of the test statistic is given by:
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is expected mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Using traditional methods, it takes 8.1 hours to receive a basic flying license.
This means that [tex]\mu = 8.1[/tex]
A researcher used the technique with 23 students and observed that they had a mean of 8.2 hours with a standard deviation of 1.2.
This means that [tex]n = 23, X = 8.2, \sigma = 1.2[/tex]
Find the value of the test statistic.
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{8.2 - 8.1}{\frac{1.2}{\sqrt{23}}}[/tex]
[tex]t = 0.4[/tex]
The value of the test statistic is 0.4.
Find the area of a rectangular carpet the measures 3 1/3 feet by 3 feet
Answer:
10 feet
Step-by-step explanation:
Which of the following is a pair of
vertical angles?
B
A
B
х
ООО
с
D
A. ZAXD and ZAXC
B. ZBXC and DXE
C. ZAXB and ZDXE
D. ZAXE and ZBXC
Answer:
B. <BXC and <DXE
Step-by-step explanation:
Vertical pair of angels are two opposite vertical angles formed when two traight lines intersect each other. They are of equal measure.
From the diagram, <BXC is vertically opposite to <DXE. Therefore they are a pair of vertical angles.
The Venn diagram below represents the students in a particular high school.
How many female students have a part-time job and a driver's license?
Female
Part-time job
74
111
56
45
92
38
137
89
Driver's license
No
Answer:
C. 45
Step-by-step explanation:
Since the question is asking how many females have both a driver's license and a part-time job. So you need to find the number that reoresents all three of these categories. This category is shown in the very center with the number 45.
Hope it helps!
Answer:
C. 45
Step-by-step explanation:
Because its inside all three circles that you want.
4 (w+1) =-6 gsdfnvbsfgbsdfbsdfb
Answer: Hello There!!
w = -5/2
Step-by-step explanation:
4(w+1)=−6
Step 1: Simplify both sides of the equation.
4(w+1)=−6
(4)(w)+(4)(1)=−6(Distribute)
4w+4=−6
Step 2: Subtract 4 from both sides.
4w+4−4=−6−4
4w=−10
Step 3: Divide both sides by 4.
4w/4 = -10/4
Answer:
-10/4
Step-by-step explanation:
4(w+1)=−6
Step 1: Simplify both sides of the equation.
4(w+1)=−6
(4)(w)+(4)(1)=−6(Distribute)
4w+4=−6
Step 2: Subtract 4 from both sides.
4w+4−4=−6−4
4w=−10
Step 3: Divide both sides by 4.
4w/4 = -10/4