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
DanielleElmas [232]
3 years ago
13

Consider the following matrix.

Mathematics
1 answer:
faltersainse [42]3 years ago
6 0

Answer:

a) the number of equations=2 and the number of variables=2

b) the system is consistent for all k , such that k≠(-2)

Step-by-step explanation:

a) for the matrix

A= \left[\begin{array}{ccc}1&k&3\\-2&4&1\end{array}\right] \\

then the number of equations = number of rows = 2 , and the number of variables = number of columns - 1 (that correspond to the independent vector or results of the equation) = 3-1 = 2

b) the system is consistent when there is at least one solution. Then the system will be inconsistent for

\left[\begin{array}{ccc}1*(-2)&k*(-2)&3*(-2)\\-2&4&1\end{array}\right] \\=\left[\begin{array}{ccc}-2&(-2k)&-6\\-2&4&1\end{array}\right] \\

for -2*k=4 → k=(-2) , the system is not consistent since the same equation -2*x + 4*y =(-6) according to the first row , while in the second row -2*x + 4*y =1  (that would mean (-6)=1 )

then the system is consistent for all k , such that k≠(-2)

-

You might be interested in
Andycycles7kilometersduringeachtriptowork. HowmanytripswillAndyhavetomaketocycleatotalof21kilometers?
Pie
Andy would have to make 3 trips in order to cycle 21 kilometers.
6 0
3 years ago
How do i solve 1/4 +1/3​
mojhsa [17]

Answer:

\large\boxed{\dfrac{1}{4}+\dfrac{1}{3}=\dfrac{7}{12}}

Step-by-step explanation:

\dfrac{1}{4}+\dfrac{1}{3}\qquad\text{find}\ LCD=(4)(3)=12\\\\=\dfrac{1\cdot3}{4\cdot3}+\dfrac{1\cdot4}{3\cdot4}=\dfrac{3}{12}+\dfrac{4}{12}=\dfrac{3+4}{12}=\dfrac{7}{12}

6 0
2 years ago
Read 2 more answers
How do you turn 4/9 into a percent
Mrrafil [7]

Answer:you divide 90 by 4

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Solve the system of equations using substitution or elimination:<br> x = 3y + 6<br> 2x - 4y = 8
dem82 [27]

Answer:

x=0, y=-2

Step-by-step explanation:

Let x=3y+6 be equation 1

and 2x-4y=8 be equation 2

sub equation 1 into equation2,

2(3y+6)-4y=8

6y+12-4y=8

2y=-4

y=-2

sub y=-2 into equation 1,

x=3(-2)+6

x=0

sub is an abbreviation for substitute

5 0
2 years ago
I HATE PROBABILITY i never got the hang of it the question is 'if the probability of rain is 0.63 what is the probability of no
kirill115 [55]

The answer would be .37, or 37%. 100 - 63 = 37.

3 0
3 years ago
Read 2 more answers
Other questions:
  • Need help asap!!!!!
    14·1 answer
  • Write an equation in slope-intercept form of the line that passes through (−2, 5) and (−4, −5).
    7·1 answer
  • justin is redoing his bathroom floor with tiles measuring 6 in. by 13 in. the floor has an area of 8,500 in2. what is the least
    10·2 answers
  • In the expression below, k is an integer.
    14·1 answer
  • What is the asymptote of the exponential function y=3^x-3
    14·1 answer
  • Taryn and Alastair both mow lawns. Each charges a flat fee to mow a lawn. The table shows the number of lawns mowed in the past
    10·2 answers
  • Which is the equation for the line that has a slope of 12 and passes through the point (3, 20)?
    8·1 answer
  • Find the opposite of the opposite of each integer.<br> 5. -4<br> 7. 8<br> 6. -15<br> 8. -7
    13·1 answer
  • If B is the midpoint of AC, and AC= 8x-20, find BC.
    5·1 answer
  • Which monomial is a perfect cube? 49p9q3r24 81p12q15r12 121p9q3r6 343p6q21r6.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!