2.3 Determine whether the following sets are linearly dependent or linearly independent. -2 { (-²3).(-²-9)} in M₂x2 (R) 4 (a) { (-² (b) { (-1 {(-1).(-2)}₁ 4 - (c) {x³ + 2x²,-x² + 3x+1, x³ = x² + 2x - 1} in P3 (R) (d) {x³x, 2x² + 4,-2x³ +3x²+2x+6} in P3 (R) (e) {(1,-1,2), (1, -2, 1), (1, 1, 4)} in R³ (f) {(1,-1,2), (2, 0, 1), (-1, 2, -1)} in R³ in M₂x2 (R) 1 (g) {(-29) (1) (1 3) (-3)} 2 (¹) { (-1² { (-21) (1 - ¹)- (- 1 3). (²2) } in M₂x2(78) (18) -2 (i) 4 in M2x2(R) {x4x³+5x²8x+6,-x² + x³ - 5x² + 5x - 3, x+3x²-3x+5, 2x4+3x³+4x²-x+1, x³x+2} in P4 (R) 3 (j) {x¹ x³ +5x²8x+6,-x4+x³5x² + 5x - 3, x4 + 3x²-3x+5,2x4+x³+4x² + 8x} in P4 (R)

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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Section 1.5: 

Exercises : 2(b,d,f) only!

2.3 Determine whether the following sets are linearly dependent or linearly
independent.
-2
{ (-²3).(-²-9)} in M₂x2 (R)
4
(a) { (-²
(b)
{ (-1
{(-1).(-2)}₁
4
-
(c) {x³ + 2x²,-x² + 3x+1, x³ = x² + 2x - 1} in P3 (R)
(d) {x³x, 2x² + 4,-2x³ +3x²+2x+6} in P3 (R)
(e) {(1,-1,2), (1, -2, 1), (1, 1, 4)} in R³
(f) {(1,-1,2), (2, 0, 1), (-1, 2, -1)} in R³
in M₂x2 (R)
1
(g) {(-29) (1) (1 3) (-3)}
2
(¹) { (-1²
{ (-21) (1 - ¹)- (- 1 3). (²2) } in M₂x2(78)
(18)
-2
(i)
4
in M2x2(R)
{x4x³+5x²8x+6,-x² + x³ - 5x² + 5x - 3,
x+3x²-3x+5, 2x4+3x³+4x²-x+1, x³x+2} in P4 (R)
3
(j) {x¹ x³ +5x²8x+6,-x4+x³5x² + 5x - 3,
x4 + 3x²-3x+5,2x4+x³+4x² + 8x} in P4 (R)
Transcribed Image Text:2.3 Determine whether the following sets are linearly dependent or linearly independent. -2 { (-²3).(-²-9)} in M₂x2 (R) 4 (a) { (-² (b) { (-1 {(-1).(-2)}₁ 4 - (c) {x³ + 2x²,-x² + 3x+1, x³ = x² + 2x - 1} in P3 (R) (d) {x³x, 2x² + 4,-2x³ +3x²+2x+6} in P3 (R) (e) {(1,-1,2), (1, -2, 1), (1, 1, 4)} in R³ (f) {(1,-1,2), (2, 0, 1), (-1, 2, -1)} in R³ in M₂x2 (R) 1 (g) {(-29) (1) (1 3) (-3)} 2 (¹) { (-1² { (-21) (1 - ¹)- (- 1 3). (²2) } in M₂x2(78) (18) -2 (i) 4 in M2x2(R) {x4x³+5x²8x+6,-x² + x³ - 5x² + 5x - 3, x+3x²-3x+5, 2x4+3x³+4x²-x+1, x³x+2} in P4 (R) 3 (j) {x¹ x³ +5x²8x+6,-x4+x³5x² + 5x - 3, x4 + 3x²-3x+5,2x4+x³+4x² + 8x} in P4 (R)
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