Which of the following statements are true I. The space P_2 is a sub.pdf

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Which of the following statements are true? I. The space P_2 is a subspace of P_3. II. The set of polynomials of the form a_2t^2 + a_1t + a_0 with a_2a_1a_0 = 0 is a subspace of P_2. III. The set of polynomials of the form a_2t^2 + a_1t + a_0 with a_2 + 2 = a_1 + a_0 + 2 is a subspace of P_2. A. I only B. II only C. I and III D. II and III E. I, II and III Solution Let us analyze all these statements one by one Statement I : We know that standard basis for P2 is {1, x, x^2} and standard basis for P3 is {1,x,x^2,x^3}. And P2 closed on vector addition, scalar multiplication over P3 (and it already contails zero vector), therefore, P2 is indeed a subspace of P3. Therefore, statement I is true. Statement II : Set of polynomials a2t2+a1t+a0 with a2a1a0 = 0 would mean that one of a2, a1 and a0 must be zero. If either of a2, a1 or a0 be zero, then using a linear combination, we can get a vector that will have all three components. But as per the given condition, our set can have polynomials with only two components. Therefore, the given set is not closed under vector addition. Therefore, Statement II is false. Statement III : Set of polynomials a2t2+a1t+a0 with a2+2 = a1+a0+2. We can write a2+2 = a1+a0+2 as a2 = a1+a0 Then, the vector a2t2+a1t+a0 becomes (a1+a0)t2+a1t+a0 This set is closed under vector addition as well as scalar multiplication and it also contains vector 0, therefore, it forms a subspace of P2. Hence statement III is true. Therefore, C is the correct option!.

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$Which of the following statements are true? I. The space P_2 is a subspace of P_3. II. The set of polynomials of the form a_2t^2 + a_1t + a_0 with a_2a_1a_0 = 0 is a subspace of P_2. III. The set of polynomials of the form a_2t^2 + a_1t + a_0 with a_2 + 2 = a_1 + a_0 + 2 is a subspace of P_2. A. I only B. II only C. I and III D. II and III E. I, II and III Solution Let us analyze all these statements one by one Statement I : We know that standard basis for P2 is {1, x, x^2} and standard basis for P3 is {1,x,x^2,x^3}. And P2 closed on vector addition, scalar multiplication over P3 (and it already contails zero vector), therefore, P2 is indeed a subspace of P3. Therefore, statement I is true. Statement II : Set of polynomials a2t2+a1t+a0 with a2a1a0 = 0 would mean that one of a2, a1 and a0 must be zero. If either of a2, a1 or a0 be zero, then using a linear combination, we can get a vector that will have all three components. But as per the given condition, our set can have polynomials with only two components. Therefore, the given set is not closed under vector addition. Therefore, Statement II is false. Statement III : Set of polynomials a2t2+a1t+a0 with a2+2 = a1+a0+2. We can write a2+2 = a1+a0+2 as a2 = a1+a0 Then, the vector a2t2+a1t+a0 becomes (a1+a0)t2+a1t+a0 This set is closed under vector addition as well as scalar multiplication and it also contains vector 0, therefore, it forms a subspace of P2. Hence statement III is true. Therefore, C is the correct option!$

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For Programming Embedded Systems Q-07 *Whcih variable and condition is sued to detect unfinished tasks (interrupted interrupt)? A) Line 28 B) Line 36 C) Line 25 D) Line 22 I. #include \"rims.h\" 2 3 4. typedef struct task state BL LedOff; break; default: int state; unsigned long period; unsigned long elapsedTime: int (*TickFct) (int); taski state ) I Transitions switch (state) case BL Ledoff: 11. task tasks [2] break; case BL Ledon: 13. const unsigned char tasksNum 2; 14. const unsigned long periodBlinkLed = 1500; 15. const unsigned long periodThreeLeds 500; break; default: break; ) // State actions 17, const unsigned long tasksPeriodGCD = 500; return state 19. int TickFct BlinkLed (int state) 20. int TickFct ThreeLeds (int state) 22. unsigned char process!ngRdyTasks = 0; 23. void TimerISR 98. enum TL States TL TO, TL T1, TL T2 TL State; 100 99. int TickFct ThreeLeds (int state) ( 101 VARIABLES MUST BE DECLARED STATIC/ unsigned char i; if (processingRdyTasks) /*e.g., static int x = 0; */ /*variables for state machine go here. printf (\"Period too short \ \"): 103 switch (state) case -1: process!ngRdyTasks = 1; for (1 = 0; 1 = 107 108 109 tasks [i].period) case TL TO: tasks [1]. state = 1 tasks[i].TickFct (tasks[i].state); state = TL T1; tasks[i].elapsedTime0 break; case TL T1: 112 113 tasks [1].elapsedTime += tasksPeriodGCD; processingRdyTasks - 0; state = TL T2 115 116 38. int main) break; case TL T2: unsigned char i=0; tasks [1]. state =-1; tasks [1].period = periodBlinkLed; tasks [1] .elapsedTime tasks [1] ·period; tasks [1].TickFct 6T1ckFct BlinkLed; 118 119 120 121 122 123 1 state = TL T0; break; default: state --1; tasks [1] , state = -1; tasks [1].period periodThreeLeas; tasks [1].elapsedTime = tasks [1].period; tasks [1].TICkFct = &TICkfct; ThreeLeas; 125 switch (state) 127 128 129 130 case TL TO: get Timerset (tasksPeriodGCD); break case TL T1: TimerOn () while (1) Sleep return 0 133 135 137 139 h break case TL T2: 61. enum BL States BL Ledoff, BL Ledon BL State; 62. int TickFct BlinkLed (int state) *VARIABLES MUST BE DECLARED STATIC break; 64. /*e.g., static Int X = 0; */ 65. /*variables for state machine go here/ default: break switch (state) case-1: return state state = BL LedOff break; 146 case BL Ledoff: state = BL Ledon; break; case BL Ledon: 1 Solution c) Line 25 is correct Line 25 contains if condition and processingRdyTasks variable is used to detect the unfinished tasks.

For Programming Embedded SystemsQ-07 Whcih variable and condition.pdf

Which of the following statements are true I. The space P_2 is a sub.pdf

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