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5) Determine Sin Szy)33 Determine the values which l and of por the following pairs equations...
10. Determine the values of k for which the system of linear equations has (i) no solution vector...
10. Determine the values of k for which the system of linear equations has (i) no solution vector, (ii) a unique solution vector, (iii) more than one solution vector (x, y, z): (a) kx+ y+ z= (b) 2x + (k-1)y + (3-k)2-1 2y + (k-3): = 2 x+ky + z = 1 -2y+ x 2x + ky- z =-2 (c) x + 2y + k= 1 (d) -3z =-3
10. Determine the values of k for which the system of...
Determine if the following pairs of lines are parallel, perpendicular or none. a) 2x + 3y...
Determine if the following pairs of lines are parallel, perpendicular or none. a) 2x + 3y = 6 3x - 2y = 6 b) y = 2x + 3 x = 2y + 3 c) x = -2 - 3y 2x + 6y = 5
3. Find m for which the following lines do not form a triangle. x+2y 5D, 2x-3y-4 .2, mx+y 0 [Sol] Since line 3 pass...
3. Find m for which the following lines do not form a triangle. x+2y 5D, 2x-3y-4 .2, mx+y 0 [Sol] Since line 3 passes through the origin, lines D, 2 and 3will not form a triangle in the following three cases: wor When D and 3 are (i) parallel. doa When 2 and 3 are (ii) parallel. When D, and 3 all intersect at one point. (ii Therefore, from ( i ), (ii) and (iii), m 4. Find a for...
SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY THE CRAMER'S METHOD 3X+5Y+3Z-12 2X+5Y-2Z-6 3x+6Y+3Z-3 a) X Y b) CHEC...
SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY THE CRAMER'S METHOD 3X+5Y+3Z-12 2X+5Y-2Z-6 3x+6Y+3Z-3 a) X Y b) CHECK YOUR RESULTS. (USE MATRICE FUNCTIONS, PRESS F2. AND THEN PRESS CTRL+SHIFT+ENTER) 3IF Y-SINC) EXPOO. INTEGRATE Y FROM X-0 Tox-1. COMPARE WITH REAL VALUE IF DX-0 a) INT b) INT ,IF DX- 005 REAL VALUE 3) Plot sin x letting maco c/ Prepave hese cuves 4) SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY INVERSE METHOD 3 X+3Z-13 2X +5 Y-2Z-2 3 X+6Y+2Z-3 Z-...
3. Consider the following system of linear equations: 2.0 + 2y + 2kz = 2 kx...
3. Consider the following system of linear equations: 2.0 + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 72 = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working. 4. Solve the following system of linear equations using Gauss-Jordan elimination: x1 + x2 - 2.13 + 24 +3.25 = 1 2.x1 - x2 +...
please show steps cleary 7. Solve the following equations for x: b)3(2x-5)-(2-3x)--2+4x 9 15 5 c)H...
please show steps cleary
7. Solve the following equations for x: b)3(2x-5)-(2-3x)--2+4x 9 15 5 c)H x-μ e) x3+8x2+15x-0 1 (4x-5)2-5-20 (use the square-root method) g) Solve using the quadratic formula: 3x2+2x -8-0. Show your steps clearly. x+4x-8-0. Show your steps clearly h) Solve by completing the Square: 8. Determine an equation for the line a) with slope of 5/3 and y-intercept of 5: b) with slope 7/6 and passing through the point (6.2) parallel to the line in #...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent p...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
Question 1 (CLO (1): S marks A) : [2.5 Marks ] In the following equations, the...
Question 1 (CLO (1): S marks A) : [2.5 Marks ] In the following equations, the symbols ak & mare constants and the rest are variables. Determine which of these equations are Linear and which are Non-Linear. Low Oway ara -ay= 22-25 O Y = 3z/k + wy(w+y-owy) 2x– Inl1 = ke + 403 - +5y ack - y)=x+3y - 2+mW 72+bx' = y +10 ............ (2) ....... (3) Linear Non-Linear Equation (1) Equation (2) Equation (3) Equation (4) Equation...
(1 point) Determine which of the following pairs of functions are linearly independent. NO_ANSWER 1. f(t)...
(1 point) Determine which of the following pairs of functions are linearly independent. NO_ANSWER 1. f(t) = 5t? + 35t, g(t) = 5t2 – 35t NO_ANSWER 2. f(t) = edt cos(ut), g(t) = edt sin(ut) ,70 NO_ANSWER 3. f(x) = 51, g(x) = 5(2-3) NO_ANSWER 4. f(t) = 3t , g(t) = 1t|
Determine the values of a for which the following system of linear equations has no solutions,...
Determine the values of a for which the following
system of linear equations has no solutions, a unique solution, or
infinitely many solutions. You can select 'always', 'never', 'a =
', or 'a ≠', then specify a value or comma-separated list of
values.
x1+ax2−x3
=
2
−x1+4x2−2x3
=
−5
−2x1+3x2+x3
=
−4
No Solutions:
Unique Solution:
Infinitely Many Solutions:
10. Determine the values of k for which the system of linear equations has (i) no solution vector, (ii) a unique solution vector, (iii) more than one solution vector (x, y, z): (a) kx+ y+ z= (b) 2x + (k-1)y + (3-k)2-1 2y + (k-3): = 2 x+ky + z = 1 -2y+ x 2x + ky- z =-2 (c) x + 2y + k= 1 (d) -3z =-3
10. Determine the values of k for which the system of...
3. Find m for which the following lines do not form a triangle. x+2y 5D, 2x-3y-4 .2, mx+y 0 [Sol] Since line 3 passes through the origin, lines D, 2 and 3will not form a triangle in the following three cases: wor When D and 3 are (i) parallel. doa When 2 and 3 are (ii) parallel. When D, and 3 all intersect at one point. (ii Therefore, from ( i ), (ii) and (iii), m 4. Find a for...
SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY THE CRAMER'S METHOD 3X+5Y+3Z-12 2X+5Y-2Z-6 3x+6Y+3Z-3 a) X Y b) CHECK YOUR RESULTS. (USE MATRICE FUNCTIONS, PRESS F2. AND THEN PRESS CTRL+SHIFT+ENTER) 3IF Y-SINC) EXPOO. INTEGRATE Y FROM X-0 Tox-1. COMPARE WITH REAL VALUE IF DX-0 a) INT b) INT ,IF DX- 005 REAL VALUE 3) Plot sin x letting maco c/ Prepave hese cuves 4) SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY INVERSE METHOD 3 X+3Z-13 2X +5 Y-2Z-2 3 X+6Y+2Z-3 Z-...
3. Consider the following system of linear equations: 2.0 + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 72 = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working. 4. Solve the following system of linear equations using Gauss-Jordan elimination: x1 + x2 - 2.13 + 24 +3.25 = 1 2.x1 - x2 +...
please show steps cleary
7. Solve the following equations for x: b)3(2x-5)-(2-3x)--2+4x 9 15 5 c)H x-μ e) x3+8x2+15x-0 1 (4x-5)2-5-20 (use the square-root method) g) Solve using the quadratic formula: 3x2+2x -8-0. Show your steps clearly. x+4x-8-0. Show your steps clearly h) Solve by completing the Square: 8. Determine an equation for the line a) with slope of 5/3 and y-intercept of 5: b) with slope 7/6 and passing through the point (6.2) parallel to the line in #...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
Question 1 (CLO (1): S marks A) : [2.5 Marks ] In the following equations, the symbols ak & mare constants and the rest are variables. Determine which of these equations are Linear and which are Non-Linear. Low Oway ara -ay= 22-25 O Y = 3z/k + wy(w+y-owy) 2x– Inl1 = ke + 403 - +5y ack - y)=x+3y - 2+mW 72+bx' = y +10 ............ (2) ....... (3) Linear Non-Linear Equation (1) Equation (2) Equation (3) Equation (4) Equation...
(1 point) Determine which of the following pairs of functions are linearly independent. NO_ANSWER 1. f(t) = 5t? + 35t, g(t) = 5t2 – 35t NO_ANSWER 2. f(t) = edt cos(ut), g(t) = edt sin(ut) ,70 NO_ANSWER 3. f(x) = 51, g(x) = 5(2-3) NO_ANSWER 4. f(t) = 3t , g(t) = 1t|
Determine the values of a for which the following
system of linear equations has no solutions, a unique solution, or
infinitely many solutions. You can select 'always', 'never', 'a =
', or 'a ≠', then specify a value or comma-separated list of
values.
x1+ax2−x3
=
2
−x1+4x2−2x3
=
−5
−2x1+3x2+x3
=
−4
No Solutions:
Unique Solution:
Infinitely Many Solutions:
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