6. For linear transformation, X=\(\begin{bmatrix}2&1&1\\1&1&2\\1&0&-2\end{bmatrix}\)Y, find Y co-ordinates for (1, 2, -1) in X.

(0, -2, 0) (-1, 3, 1) (-1, -2, 0) (-1, 3, 0)

Hint Answer

7. Find value of non singular matrices P and Q, such that PAQ is in normal form, where A is
\(\begin{bmatrix}1&1&2\\1&2&3\\0&-1&-1\end{bmatrix}\)

\(\begin{bmatrix}1&0&0\\-1&1&0\\-1&1&1\end{bmatrix}\), \(\begin{bmatrix}1&-1&-1\\0&1&-1\\0&0&1\end{bmatrix}\) \(\begin{bmatrix}1&1&0\\-1&1&0\\-1&1&1\end{bmatrix}\), \(\begin{bmatrix}1&-1&-1\\0&1&-1\\0&0&1\end{bmatrix}\) \(\begin{bmatrix}1&0&0\\-1&1&0\\-1&1&1\end{bmatrix}\), \(\begin{bmatrix}1&-1&1\\0&1&-1\\0&0&1\end{bmatrix}\) \(\begin{bmatrix}1&0&0\\-1&1&0\\-1&0&1\end{bmatrix}\), \(\begin{bmatrix}1&-1&-1\\0&1&-1\\0&0&-1\end{bmatrix}\)

Hint Answer

8. Test for consistency and solve system of equations if possible to get value of z.

2x - 3y+ 7z = 5
3x + y - 3z = 13
2x + 19y - 47z = 32

Consistent, z = -1 Consistent, z = 0 Inconsistent Consistent, z = 5

Hint Answer

9. Find value of z that satisfies all given equations using Gauss Elimination Method.

12x + 4y + 3z = -1
3x + 8y + z = 2
2x + 3y + 4z = 5

z=\(\frac{53}{41}\) z=\(\frac{-143}{287}\) z=\(\frac{79}{287}\) z=\(\frac{-53}{41}\)

Hint Answer

10. Solve following equations using Gauss Elimination Method.

x + 2y + 3z = 4
2x + 3y + 4z = 5
3x + 4y + 5z = 6

x=0.5 y=0 and z=1 x=-0.5 y=0 and z=-1.5 x=-0.5 y=0 and z=1.5 x=0.5 y=0 and z=1.5

Hint Answer

11. Find value of x and y that satisfy given sets of equation using Gauss Elimination Method.

2x - 3y + 2z - 2w = 4
3x + 2y - 3z + 5w = 1
4x + 5y + 11z + 3w = 3
5x + 3y + 2z + 7w = - 1

x=0.85 and y=-1.2 x=0.85 and y=0.38 x=0.27 and y=0.38 x=0.27 and y=-1.2

Hint Answer

12. Fit a straight line y=a+bx into given data:
(x,y):(5,12)(10,13)(15,14)(20,15)(25,16).

y=11 y=0.2x y=11+0.2x y=1.1+0.2x

Hint Answer

13. Fit a straight line y=a+bx into given data by Actual Mean Method. What is value of b?

x: 10 20 30 40 50

y: 22 23 27 28 30

1.2 0.15 0.21 0.8

Hint Answer

14. Fit a straight line y=a+bx into given data. Also estimate production in year 2000.

Year(x): 1966 1976 1986 1996 2006

Production in lbs(y): 10 12 13 16 17

12.33 14.96 11.85 18.67

Hint Answer

15. Fit a straight line y=a+bx into given data. What is value of y when x=8 ?

x: 1 2 3 4 5 6

y: 20 21 22 23 24 25

45.2 26 28 37

Hint Answer

Nexttt

x	y	x²	xy
5	12	25	60
10	13	100	130
15	14	225	210
20	15	400	300
25	16	625	400
∑x=75	∑y=70	∑x²=1375	∑xy=1100

x	y	X=x-30	Y=y-26	X²	XY
10	22	-20	-4	400	80
20	23	-10	-3	100	30
30	27	0	1	0	0
40	28	10	2	100	20
50	30	20	4	400	80
		∑X=0	∑Y=0	∑X²=1000	∑XY=210

x	y	X=x-1986	Y=y-13	X²	XY
1966	10	-20	-3	400	60
1976	12	-10	-1	100	10
1986	13	0	0	0	0
1996	14	10	1	100	10
2006	16	20	3	400	60
		∑X=0	∑Y=0	∑X² =1000	∑XY=140

x	y	x²	xy
1	20	1	20
2	21	4	42
3	22	9	66
4	23	16	92
5	24	25	125
6	25	36	216
∑x=21	∑y=135	∑x²=91	∑xy=561

Guest You need to login to ask any Questions from chapter Laplace-Transform of

Chapter:

(-1, 3, 0)

\(\begin{bmatrix}1&0&0\\-1&1&0\\-1&1&1\end{bmatrix}\), \(\begin{bmatrix}1&-1&-1\\0&1&-1\\0&0&1\end{bmatrix}\)

Inconsistent

z=\(\frac{53}{41}\)

x=-0.5 y=0 and z=1.5

x=0.27 and y=-1.2

y=11+0.2x

0.21

14.96

26

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Matrices

For linear transformation, X=\(\begin{bmatrix}2&1&1\\1&1&2\\1&0&-2\end{bmatrix}\)Y, find Y co-ordinates for (1, 2, -1) in X.

Find value of non singular matrices P and Q, such that PAQ is in normal form, where A is \(\begin{bmatrix}1&1&2\\1&2&3\\0&-1&-1\end{bmatrix}\)

Test for consistency and solve system of equations if possible to get value of z. 2x - 3y+ 7z = 5 3x + y - 3z = 13 2x + 19y - 47z = 32

Find value of z that satisfies all given equations using Gauss Elimination Method. 12x + 4y + 3z = -1 3x + 8y + z = 2 2x + 3y + 4z = 5

Solve following equations using Gauss Elimination Method. x + 2y + 3z = 4 2x + 3y + 4z = 5 3x + 4y + 5z = 6

Find value of x and y that satisfy given sets of equation using Gauss Elimination Method. 2x - 3y + 2z - 2w = 4 3x + 2y - 3z + 5w = 1 4x + 5y + 11z + 3w = 3 5x + 3y + 2z + 7w = - 1

Fit a straight line y=a+bx into given data: (x,y):(5,12)(10,13)(15,14)(20,15)(25,16).

Fit a straight line y=a+bx into given data by Actual Mean Method. What is value of b? x: 10 20 30 40 50 y: 22 23 27 28 30

Fit a straight line y=a+bx into given data. Also estimate production in year 2000. Year(x): 1966 1976 1986 1996 2006 Production in lbs(y): 10 12 13 16 17

Fit a straight line y=a+bx into given data. What is value of y when x=8 ? x: 1 2 3 4 5 6 y: 20 21 22 23 24 25

Guest
You need to login to ask any Questions from chapter Laplace-Transform of

Find value of non singular matrices P and Q, such that PAQ is in normal form, where A is
\(\begin{bmatrix}1&1&2\\1&2&3\\0&-1&-1\end{bmatrix}\)

Test for consistency and solve system of equations if possible to get value of z.

2x - 3y+ 7z = 5 3x + y - 3z = 13 2x + 19y - 47z = 32

Find value of z that satisfies all given equations using Gauss Elimination Method.

12x + 4y + 3z = -1 3x + 8y + z = 2 2x + 3y + 4z = 5

Solve following equations using Gauss Elimination Method.

x + 2y + 3z = 4 2x + 3y + 4z = 5 3x + 4y + 5z = 6

Find value of x and y that satisfy given sets of equation using Gauss Elimination Method.

2x - 3y + 2z - 2w = 4 3x + 2y - 3z + 5w = 1 4x + 5y + 11z + 3w = 3 5x + 3y + 2z + 7w = - 1

Fit a straight line y=a+bx into given data:
(x,y):(5,12)(10,13)(15,14)(20,15)(25,16).

Fit a straight line y=a+bx into given data by Actual Mean Method. What is value of b?

x: 10 20 30 40 50

y: 22 23 27 28 30

Fit a straight line y=a+bx into given data. Also estimate production in year 2000.

Year(x): 1966 1976 1986 1996 2006

Production in lbs(y): 10 12 13 16 17

Fit a straight line y=a+bx into given data. What is value of y when x=8 ?

x: 1 2 3 4 5 6

y: 20 21 22 23 24 25