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
OLEGan [10]
1 year ago
12

(1 point) The matrix 6 4 -7 k is invertible if and only if k is not equal to

Mathematics
1 answer:
alisha [4.7K]1 year ago
7 0

Answer:

  k ≠ -14/3

Step-by-step explanation:

A square matrix is invertible if and only if its determinant is not zero.

<h3>Determinant</h3>

The determinant of a 2×2 matrix is the difference of the products of the diagonal terms and the off-diagonal terms:

  det = (6)(k) -(-7)(4) = 6k +28

<h3>Restriction on k</h3>

The requirement that the determinant is not zero places a restriction on k.

  6k +28 ≠ 0

  k +14/3 ≠ 0 . . . . . . divide by 6

  k ≠ -14/3 . . . . . . . . subtract 14/3

For the matrix to be invertible, the value of k must not be -14/3.

You might be interested in
Can someone help me with this?
erik [133]

The equilibrium price is $12.

<h3>What is the equilibrium price ?</h3>

Equilibrium is the point where the quantity demanded is equal to the quantity supplied. The price at equilibrium is known as the equilibrium price and the quantity at equilibrium is known as the equilibrium quantity.

When shown on a graph, equilibrium is the point where the quantity demanded curve is equal to the quantity supplied curve.

When there is equilibrium, the equation of quantity demanded would be equal to the equation of quantity supplied.

-280 + 40p = 800  - 50p

In order to determine the value of p, take the following steps:

Combine similar terms: 800 + 280 = 40p + 50p

Add similar terms = 1080 = 90p

Divide both sides of the equation by 90 : 1080 / 90 = 12

To learn more about equilibrium, please check: brainly.com/question/26075805

#SPJ1

7 0
1 year ago
The perimeter of a rectangle is 62 m. The length is four more than two times the width. What is the length?
Travka [436]
--------------------------------------------------
Define length and width
--------------------------------------------------
Let x be the width
width = x
Length = 2x + 4

--------------------------------------------------
Formula
--------------------------------------------------
Perimeter = 2(length + width)

--------------------------------------------------
Find Length and width
--------------------------------------------------
62 = 2(2x + 4 + x)
62 = 2(3x + 4)            <em> ← combine like terms  </em> 
62 = 6x + 8                 <em>← remove bracket </em>  
62 - 8 = 6x                  <em>← minus 8 on both sides </em>
6x = 54                      <em> ← swap sides  </em>
x = 54 ÷ 6                   <em>← divide by 6 on both sides</em>
<em>x = 9 m</em>

--------------------------------------------------
Find Length and Width
--------------------------------------------------
Width = x = 9 m
Length = 2x + 4 = 2(9) + 4 = 22 m

--------------------------------------------------
Answer: Length = 22m
--------------------------------------------------
3 0
3 years ago
Read 2 more answers
You need to buy 12 pounds of chicken for a barbecue that you are planning. You found an ad in the Northwest Florida Daily News t
Keith_Richards [23]

Answer:

yes

Step-by-step explanation:

The difference in the cost per pound is $6.

For 12 lb, the total difference in $6 × 12 = $72.

If the Fresh Market is close enough and you have the time, it is worth the drive since you will save $72.

5 0
2 years ago
One of the problems with our current election system is??
12345 [234]

Answer:

Assuming you mean the US election a problem with our electron is the person who wins the most popular vote doesn't always win.

Why is this a problem?

We vote for who we want as a president as it should work, but then the most elected doesn't always become president. Almost like our votes do not matter and is very discouraging.

Hope this helps!

-Payshence


5 0
3 years ago
19. The bases of a trapezoid are 8 and 22 and the trapezoid's area is 135. Find the height
julia-pushkina [17]

Answer: 9

Step-by-step explanation:

A=(a+b)/2 *h

135= 30/2* h

135= 15 * h

135/15= h

9=h

8 0
3 years ago
Read 2 more answers
Other questions:
  • vinny invested $25,000 in an account that earns 4.25% simple interest. if vinny doesn't make any additional deposits or withdraw
    15·1 answer
  • Which probability method involves estimating a probability by using personal judgment or an educated​ guess?
    7·1 answer
  • StephanieHad 7/8 pound of bird seed she can use 3/8 pound to fill a bird feeder how much birdseed to Stephanie have left
    10·1 answer
  • Lex is at the mall, which is 8 miles from his house. Lex walks home at a constant rate of 2 miles an hour.
    8·1 answer
  • Solve by factoring: 2sinxcosx=sinx in [0,2π)
    15·1 answer
  • M(x)=x^2-3x<br> N(x)=x-5<br><br> MN(-1)= ?<br><br> A.18<br> B.-20<br> C.-22<br> D. -24
    7·1 answer
  • The cost C, in dollars, for a health club membership depends on the number m of whole months you join. This situation is represe
    15·1 answer
  • He two square roots of the number.<br><br> 64
    12·2 answers
  • PLEASE I don't understand how to do this, 50 Points for anyone who solves it!
    10·1 answer
  • Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. x+7–4x3​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!