1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anna [14]
3 years ago
9

Which of the following statements are true about scalar multiplication of matrices?

Mathematics
2 answers:
VashaNatasha [74]3 years ago
6 0

Consider all options:

1. You can multiply a matrix of any size by a scalar. This option is true, because the rule of multiplication matrix by the number k, where k≠0 (according to definition) is

k\cdot \left(\begin{array}{ccc}a_{11} & \dots & a_{1n}\\& \dots & \\a_{m1} & \dots & a_{mn}\end{array}\right)=\left(\begin{array}{ccc}ka_{11} & \dots & ka_{1n}\\& \dots & \\ka_{m1} & \dots & ka_{mn}\end{array}\right).

2. For any matrix A, 1 × A = A. This option is true, because according to previous definition

1\cdot A=1\cdot \left(\begin{array}{ccc}a_{11} & \dots & a_{1n}\\& \dots & \\a_{m1} & \dots & a_{mn}\end{array}\right)=\left(\begin{array}{ccc}1\cdot a_{11} & \dots & 1\cdot a_{1n}\\& \dots & \\1\cdot a_{m1} & \dots & 1\cdot a_{mn}\end{array}\right)=\left(\begin{array}{ccc}a_{11} & \dots & a_{1n}\\& \dots & \\a_{m1} & \dots & a_{mn}\end{array}\right)=A.

3. For any scalar r, rI = I, where I is the identity matrix. This option is false, for example

r\cdot \left(\begin{array}{cc}1 &0\\0 & 1\end{array}\right)= \left(\begin{array}{cc}r &0\\0 & r\end{array}\right)\neq \left(\begin{array}{cc}1 &0\\0 & 1\end{array}\right).

4. You can scale geometric figures using scalar multiplication. Geometric figures consists of points and their coordinates can be considered as matrices. Using scalar multiplication to these matrices you'll get coordinates of image figures.

This option is true.

5. Scalar multiplication is a shortcut for repeated addition of the same matrix. While adding matrices you add the corresponding numbers (a_{ij} to a_{ij}), then for each matrix's element you can use  multiplication as a shortcut for repeated addition and then get  multiplication as a shortcut for repeated addition for whole matrix.

6. Scalar multiplication is not possible for matrices that are not square. This is not true, because the definition says that multiplication matrix by a scalar is possible for all matrices.

Answer: correct options are 1, 2, 4 and 5.


Greeley [361]3 years ago
3 0

Scalar multiplication of a matrix refers to the multiplication of all the elements of the matrix by an ordinary number which is called a scalar.

From the given options the statements which are true about scalar multiplication of matrices are;

a)       You can multiply a matrix of any size by a scalar.

b)      For any matrix A, 1 × A = A.

c)       Scalar multiplication is a shortcut for repeated addition of the same matrix.

You might be interested in
What two number multiplied equal 12 but also added together equal -7
FromTheMoon [43]
A) x * y = 12
B) x + y = -7
A) x = 12 / y
Substitute this into B
B) 12/y + y = -7
multiplying both sides by "y"
12 + y^2 = -7y
y^2 + 7y + 12 = 0
y = -4
and from equation B we calculate x as -3



7 0
3 years ago
Solve for d. 1.2+d+0.4=9.7
Advocard [28]
Move everything around. d+1.6=9.7. d=8.1.
3 0
3 years ago
Read 2 more answers
On the unit circle, where I <0<2, when is tan 0 undefined?
Ilya [14]

Answer:

can you please be more specific? Maybe add more info.

Step-by-step explanation:

7 0
3 years ago
Suppose that 12% of test scores for the unit 1 test were above 85 and 8% were below 70. Assuming a normal
Doss [256]

Answer:

Mean = 78.2

Standard deviation = 5.8

Step-by-step explanation:

Mathematically z-score;

= (x-mean)/SD

From the question;

12% of test scores were above 85

Thus;

P( x > 85) = 12%

P(x > 85) = 0.12

Now let’s get the z-score that has a probability of 0.12

This can be obtained from the standard normal distribution table and it is = 1.175

Thus;

1.175 = (85 - mean)/SD

let’s call the mean a and the SD b

1.175 = (85-a)/b

1.175b = 85 - a

a = 85 - 1.175b ••••••••(i)

Secondly 8% of scores were below 70

Let’s find the z-score corresponding to this proportion;

We use the standard normal distribution table as usual;

P( x < 70) = 0.08

z-score = -1.405

Thus;

-1.405 =( 70-a)/b

-1.405b = 70-a

a = 70 + 1.405b ••••••(ii)

Equate the two a

70 + 1.405b = 85 - 1.175b

85 -70 = 1.405b + 1.175b

15 = 2.58b

b = 15/2.58

b = 5.81

a = 70 + 1.405b

a = 70 + 1.405(5.81)

a = 78.16

So mean = 78.2 and Standard deviation is 5.8

4 0
3 years ago
Two buses are traveling the same route toward a hotel. Bus 1 travels at a rate of 55 miles per hour This is bus two:
Charra [1.4K]

Answer:

Bus 1 is traveling faster.

Step-by-step explanation:

The information provided states that Bus 1 travels at 55 miles per hour. The graph shows that Bus 2 travels less than 50 miles per hour. This shows that Bus 1 travels more miles per hour.

Hope it helps!

3 0
2 years ago
Other questions:
  • HURRY WILL GIVE BRAINIEST!!!!!
    8·1 answer
  • Whats the product for (2z-3)^3
    14·2 answers
  • Is the following relation a function?
    5·2 answers
  • What are the exact solutions of x2 − 5x − 7 = 0, where x equals negative b plus or minus the square root of b squared minus 4 ti
    8·2 answers
  • James rode his bike for 0.65 hours and traveled 8.45 km what is his speed?
    12·1 answer
  • you can use a calculator if you want. No links please help this is very important i will give you brain thing if its correct
    11·2 answers
  • Jonah has been saving for a video game. Last year it cost $28. This year it costs $36. Determine the percent of change.​
    6·1 answer
  • Can anyone help me solve this?​
    9·2 answers
  • Find the Arc Length AND Sector Area from the circle. Use 3.14 for pi. Do not round your answer.
    8·2 answers
  • Explain how to find the value of the digit 7 in the number 3,684,591.74.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!