Vector equation

Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent

Result

c1 = (Correct answer is: ) OK
c2 = (Correct answer is: 2 c1) Wrong answer
c3 = (Correct answer is: -c1) Wrong answer

Solution:

c1 1+c2 0+c3 1=0 c1 2+c2 (1)+c3 0=0 c1 1+c2 3+c3 7=0  c1+c3=0 2 c1c2=0 c1+3 c2+7 c3=0  c1=any c2=2 c1 c1=c3=c1c_{1} \cdot \ 1+c_{2} \cdot \ 0+c_{3} \cdot \ 1=0 \ \\ c_{1} \cdot \ 2+c_{2} \cdot \ (-1)+c_{3} \cdot \ 0=0 \ \\ c_{1} \cdot \ 1+c_{2} \cdot \ 3+c_{3} \cdot \ 7=0 \ \\ \ \\ c_{1} + c_{3}=0 \ \\ 2 \ c_{1} - c_{2}=0 \ \\ c_{1} + 3 \ c_{2} + 7 \ c_{3}=0 \ \\ \ \\ c_{1}=any \ \\ c_{2}=2 \ c_{1} \ \\ c_{1}=c_{3}=-c_{1}
c2=2 c1c_{2}=2 \ c_{1}
c3=c1c_{3}=-c_{1}



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 2 comments:
#
Matematik
linearly independent

#
Math student
c1 = (Correct answer is: ) OK
c2 = (Correct answer is: 2 c1) Wrong answer
c3 = (Correct answer is: -c1) Wrong answer

avatar









Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Faces diagonals
    cuboid_1 If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2
  2. Two chords
    tetivy Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
  3. Geometric progressiob
    eq2 If the sum of four consective terms of geometric progression is 80 and arithmetic mean of second and fourth term is 30 then find terms?
  4. GP - three members
    progression_ao The second and third of a geometric progression are 24 and 12(c+1) respectively, given that the sum of the first three terms of progression is 76 determine value of c
  5. Hyperbola equation
    hyperbola_4 Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
  6. Rectangular triangle
    rt_triangle_2 The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
  7. Right triangle eq2
    rt_triangle_1 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
  8. Digit sum
    number_line_3 The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
  9. Cuboid walls
    cuboid_9 Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm².
  10. The gardener
    stromy_3 The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?
  11. Block or cuboid
    cuboid The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
  12. Volume of wood
    wood Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
  13. Growth of wood
    wood The annual growth of wood in the forest is estimated at 2%. In how many years will make the forest volume double?
  14. The Hotel
    hotel-montfort-tatry-2_2 The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numbers sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in
  15. MO Z8-I-1 2018
    age_6 Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
  16. Sales of products
    cukriky_9 For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold?
  17. Segments
    segments Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?