1,328 prompts matching "Practice: The probability of drawing one ball of each colour"
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Multiply matrices step by step #6
I am in SS 3. Show me how to multiply A=[[1,2,3]] (1x3) and B=[[1],[2],[3]] (3x1) using th
Evaluate a 3x3 determinant by expansion #2
Give me a 3x3 matrix like A=[[2,0,-1],[3,1,2],[-1,4,0]] and ask me to evaluate its determi
Evaluate a 3x3 determinant by expansion #3
I am in SS 3. Give me a 3x3 matrix like A=[[1,-2,3],[4,0,1],[2,1,-3]] and ask me to evalua
Evaluate a 3x3 determinant by expansion #4
I am in SS 3. Give me a 3x3 matrix like A=[[3,1,2],[0,-1,4],[2,3,1]] and ask me to evaluat
Spot my mistake in a determinant expansion
I am in SS 3. I expanded a 3x3 determinant along the first row but I think I mixed up a si
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
Explain why a matrix with zero determinant has no inverse
I am in SS 3. Explain why a matrix cannot be inverted when its determinant is zero, and gi
Spot my mistake in finding a matrix inverse
I found the inverse of a 2x2 matrix but I think I mixed up the sign or swapped the wrong d
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
Quiz me on equilibrium conditions
I am in SS 3. Quiz me with two short problems testing whether a set of forces is in equili
Vector addition, subtraction and magnitude #3
I am in SS 3. Give me a vector problem where a = 5i - j, find the magnitude of a. Let me a
Vector addition, subtraction and magnitude #4
I am in SS 3. Give me a vector problem where a = 2i + 3j - 6k, find the magnitude of a. Le
Vector addition, subtraction and magnitude #5
I am in SS 3. Give me a vector problem where a = 4i - 3j, find a unit vector in the direct
Spot my mistake finding a vector magnitude
I am in SS 3. I calculated the magnitude of a 3D vector but I'm not confident I squared an
Explain parallel and perpendicular vectors
I am in SS 3. Explain how to test whether two vectors are parallel or perpendicular using
Find and classify stationary points #1
I am in SS 3. Give me a calculus problem where y = x^3 - 3x^2 - 9x + 5, find and classify
Find and classify stationary points #2
I am in SS 3. Give me a calculus problem where y = 2x^3 - 15x^2 + 24x, find the stationary
Find and classify stationary points #3
I am in SS 3. Give me a calculus problem where a curve y = x^2 - 4x + 7, find the minimum