1,333 prompts matching "Why a rational number added to an irrational one stays irrational"
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Evaluate a 3x3 determinant by expansion #5
Give me a 3x3 matrix like A=[[5,-1,0],[2,3,1],[-2,0,4]] and ask me to evaluate its determi
Explain the rule of signs for determinants
Explain the checkerboard pattern of positive and negative signs used when expanding a 3x3
Solve simultaneous equations with Cramer's rule (order 2) #1
I am in SS 3. Use Cramer's rule to solve 2x + 3y = 7 and x - y = 1. Set up the coefficient
Solve simultaneous equations with Cramer's rule (order 2) #2
I am in SS 3. Use Cramer's rule to solve 3x - y = 5 and 2x + 4y = 6. Set up the coefficien
Solve simultaneous equations with Cramer's rule (order 2) #3
Use Cramer's rule to solve x + 2y = 8 and 3x - y = 3. Set up the coefficient determinant a
Solve simultaneous equations with Cramer's rule (order 2) #4
Use Cramer's rule to solve 5x + 2y = 16 and x - 3y = -7. Set up the coefficient determinan
Solve a 3x3 simultaneous equation system with Cramer's rule #1
I am in SS 3. Use Cramer's rule to solve the system x + y + z = 6, 2x - y + z = 3, x + 2y
Solve a 3x3 simultaneous equation system with Cramer's rule #2
I am in SS 3. Use Cramer's rule to solve the system 2x + y - z = 5, x - y + 2z = 1, 3x + 2
Solve a 3x3 simultaneous equation system with Cramer's rule #3
Use Cramer's rule to solve the system x - 2y + z = -1, 3x + y - z = 8, 2x - y + 3z = 5. Sh
WAEC past-question practice: determinants #2
I am in SS 3. Set me a WAEC-style question that uses Cramer's rule to solve a pair of simu
WAEC past-question practice: determinants #3
I am in SS 3. Give me a WAEC Further Mathematics exam-style question applying Cramer's rul
WAEC past-question practice: determinants #4
I am in SS 3. Test me with a timed WAEC-style determinant question — give it to me cold, l
Find the inverse of a 3x3 matrix using cofactors #1
I am in SS 3. Give me a 3x3 matrix like A=[[1,2,3],[0,1,4],[5,6,0]] and guide me through f
Find the inverse of a 3x3 matrix using cofactors #2
I am in SS 3. Give me a 3x3 matrix like A=[[2,0,1],[1,3,-1],[0,1,2]] and guide me through
Find the inverse of a 3x3 matrix using cofactors #3
Give me a 3x3 matrix like A=[[1,-1,2],[0,2,1],[3,0,1]] and guide me through finding its in
Solve simultaneous equations using an inverse matrix #1
I am in SS 3. Show me how to write 2x + 3y = 7 and x - y = 1 as a matrix equation, find th
Solve simultaneous equations using an inverse matrix #2
I am in SS 3. Show me how to write 4x + y = 9 and 2x + 3y = 8 as a matrix equation, find t
Solve simultaneous equations using an inverse matrix #3
Show me how to write 3x - 2y = 4 and x + y = 6 as a matrix equation, find the inverse of t
Define mass, force and weight with correct units
I am in SS 3. Ask me to define mass, force and weight, state the SI unit of each, and expl
Define particle and rigid body in mechanics
Ask me to explain the difference between a particle and a rigid body in mechanics, with an