- ....... is used to represent space in the matrix
14 ................6
5x-3 ............8
What value of x will this matrix be singular?
- What values of p will make this matrix singular
6p + 2 .........8
5 ...................3p
- Can a singular matrix have an inverse, justify your answer?
- Tom bought 6 plums and 5 mangoes for $40. Jane bought 3 similar plums and 4 similar mangoes for $23. Using the matrix method determine the price of 1 plum and the price of 1 mango.
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ReplyDeleteWhat values of p will make this matrix singular
ReplyDelete6p + 2 .........8
5 ..............3p
The same method above implies for this question.
Someone else give it a try.
Question 1
ReplyDelete14 ..............6
5x-3 ............8
What value of x will this matrix be singular?
So we all know that when a matrix is singular the determinant is = 0. And to find the determinant it the Major - Minor
So
Major - Minor = 0
for the question above i completed is as:
ReplyDelete14 * 8 = 112............major
since the major and minor must be cancelled off to make 0
I then divided 112 by 6
In other words, this is the value in which 5x - 3 such be multiplied by.
112/ 6 = 18.67
Now the equation is formed
5x - 3 = 18.67
5x = 21.67
x = 21.67/3
x = 4.33
Now i work it back out to see if am correct
Major - Minor = 0
14 x 8 - 6 x 5x-3 = 0
Substitute the value of x
14 x 8 - 6 x 5(4.33)-3 = 0
112 - 111.9 = 0.1
0.1 to the nearst value = 0
thats the closed i got
For question 2, am getting a lot of problems in thoses types of questions,, can someone show me how its done using step for step so i can try some....
ReplyDeleteI don't think a singular matrix has an inverse since it is already in forms of ones and zeroes.
ReplyDeletei will give it a try ok 'SWANKY THING"
ReplyDelete6p + 5m = 40 ( TOm )
3p + 4m = 23 ( Jane)
putting it into matrix form
A B C
(6 5) (p) = (40)
(3 4) (m) (23)
*hope u understand that i tried the best i can
find inverse = 1/determinate X (4 -5)
(-3 6)
move around the major and negate the minor
determinate = major - minor
= ( 4 X 6) - (5 X 3)
= 24 - 15
= 9
then multiple both sides by the inverse
and any matrix X the inverse always = 1
therefore matrix A X inverse = (1 0)
(0 1)
then u end up with
(1 0) X (p) = 1/9 (4 -5) X (40)
(0 1) (m) (-3 6) (23)
it works out to be
(p) = 1/9 (45)
(m) (18)
p = 5
m = 2
to summarize
ReplyDeleteSTEPS :
1) Write in matrix form
2) Find inverse with determinate
3) Multiple both sides by inverse which then evaluates the answers
* do u understand now ??
Question 1
ReplyDelete14 (6)
5x-3 (8)
What value of x will this matrix be singular?
So we all know that when a matrix is singular the determinant is = 0. And to find the determinant it the (Major - Minor)
Therefore:
Major - Minor = 0
6p + 5m = 40 ( TOm )
ReplyDelete3p + 4m = 23 ( Jane)
putting it into matrix form
A B C
(6 5) (p) = (40)
(3 4) (m) (23)
*hope u understand that i tried the best i can
find inverse = 1/determinate X (4 -5)
(-3 6)
move around the major and negate the minor
determinate = major - minor
= ( 4 X 6) - (5 X 3)
= 24 - 15
= 9
then multiple both sides by the inverse
and any matrix X the inverse always = 1
therefore matrix A X inverse = (1 0)
(0 1)
then u end up with
(1 0) X (p) = 1/9 (4 -5) X (40)
(0 1) (m) (-3 6) (23)
it works out to be
(p) = 1/9 (45)
(m) (18)
p = 5
m = 2
Yea i believe so....Have to practice doh
ReplyDelete(6 5) (x) (40)
ReplyDelete(3 4) (y) (23)
6x + 5y = 40
3x + 4y = 23
Matrix multiply by inverse = identity
(1 0)
(0 1)
determinant is obtained from subtracting the minor from the major.
(6 x 4) - (5 x 3)
24 - 15
9
1/9 (4 -5)
(-3 6)
1/9 (6 5) (4 -5)
(3 4) (-3 6)
(6 x 4 + 5 x -3 6 x -5 + 5 x 6)
(3 x 4 + 4 x -3 3 x -5 + 4 x 6)
( 24 - 15 -30 + 30)
( 12 - 12 -15 + 24)
1/9 (9 0)
(0 9)
(1 0)
(0 1)
(1 0) (x) = 1/9 (4 -5) (40)
(0 1) (y) (-3 6) (23)
(x) = (4 -5) (40)
(y) (-3 6) (23)
1/9 ( 4 x 40 -5 x 23)
(-3 x 40 6 x 23)
1/9 ( 160 -115)
(-120 + 138)
1/9 (45)
(18)
(5)
(2)
For the following question I read swanky things solution and she me reason to agree with her solution.
ReplyDelete14 ..............6
5x-3 ............8
Someone else may prove us wrong.
14.............6
ReplyDelete5x-3...........8
to work out a ques like this you first have to know what is a singualr matrix, then what is the major and what is the minor.
then you get 14*8 - major
6(5x-3)- minor then yo can find x
5x-3*6= 0
6p + 5m = 40 ( Tom)
ReplyDelete3p + 4m = 23 ( Jane)
matrix form
(6 5) (p) = (40)
(3 4) (m) (23)
determinant= ad-bc
6*4 - 5*3 = 9
inverse= 1/det * (d -b)
(-c a)
same as ( 4 -5)
(-3 6)
therefore the inverse = 1/9 * ( 4 -5)
(-3 6)
then u multiply the matrix * inverse
1/9 * ( 4 -5) * (6 5)
(-3 6) (3 4)
then u work it out and ul find p and m
i dont really understand d 1st two..
ReplyDeleteok johnsmith i'll try it your way
ReplyDelete6p + 5m = 40 ( TOm )
ReplyDelete3p + 4m = 23 ( Jane)
1) Write in matrix form
A B C
(6 5) (p) = (40)
(3 4) (m) (23)
2) Find inverse with determinate
= 1/determinate X (4 -5)
(-3 6)
minor determinate = major - minor
= ( 4 X 6) - (5 X 3)
= 24 - 15
= 9
3) Multiple both sides by inverse which then evaluates the answers
matrix A X inverse = (1 0)(0 1)
so (1 0) X (p) = 1/9 (4 -5) X (40)(0 1) (m)(-3 6)(23)
therefore (p) = 1/9 (45)(m) (18)
p = 5
m = 2
but torbo won't u have to find the determinent A and multipy it by c to get B
ReplyDeleteI still cannot understand what it is that you have to do in number one.
ReplyDeletea singular matrix is when the determinant is equal to 0. is AD- BC=0 (a b)
ReplyDelete(c d)
but i dont understant the first question either
i dont hthink it singular matrix could have an inverse bou i not 100% sure y not!
ReplyDeleteWll "low rider" you have to find out if the matrix is singular and this is found by the
ReplyDeletemajor - minor = det
once it is equal to 0, then the matrix is singular
Ok swanky thing i think i understand.
ReplyDelete14 ................6
ReplyDelete5x-3 ............8
now to find the value of x that will make this matrix singular, the major - minor = zero. because a singular matrix has a determinant of zero.
determinant = 14*8 - 6*(5x-3)= 0
112 - (30x+18)= 0
112 - 30x + 18 = 0
112 + 18 = 30x
130 = 30x
x = 130/30 = 4.33