1,328 prompts matching "Practice: A cubic with one real root and two complex ones"
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Scalar multiplication of a matrix #5
I am in SS 3. Set me a scalar multiplication question like A=[[0,-4,1],[2,1,-2],[3,0,5]],
Spot my mistake in a matrix transpose
I am in SS 3. I found the transpose of A=[[1,2,3],[4,5,6]] as [[1,4],[2,5],[3,6]] — please
Evaluate a 2x2 determinant #2
I am in SS 3. Give me a 2x2 matrix like A=[[7,-2],[3,1]] and ask me to evaluate its determ
Evaluate a 2x2 determinant #4
Give me a 2x2 matrix like A=[[-3,2],[4,-5]] and ask me to evaluate its determinant using a
Evaluate a 2x2 determinant #6
I am in SS 3. Give me a 2x2 matrix like A=[[0,-4],[6,2]] and ask me to evaluate its determ
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 #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
Explain the rule of signs for determinants
Explain the checkerboard pattern of positive and negative signs used when expanding a 3x3
Show all working: evaluate a 3x3 determinant
Give me a Cambridge Additional Mathematics style 3x3 determinant question that says 'show
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
Explain the adjoint of a matrix
Explain what the adjoint of a matrix is and how it relates to the matrix of cofactors, usi
Verify A times A-inverse equals the identity
I am in SS 3. Give me a 2x2 matrix and its inverse, ask me to multiply them together, and
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 a 3x3 system using the inverse matrix method #1
Show me how to solve the system x+y+z=6, 2x-y+z=3, x+2y-z=2 by writing it as AX=B, finding
Quiz me on units of force
Quiz me on the SI unit of force and how it is derived from mass and acceleration, then giv
Solve a binomial probability problem #2
Give me a binomial distribution problem where n=10, p=0.5, find P(X is at least 7), using
Solve a binomial probability problem #4
I am in SS 3. Give me a binomial distribution problem where n=12, p=0.4, find P(X=5), usin
Solve a binomial probability problem #5
I am in SS 3. Give me a binomial distribution problem where n=5, p=0.6, find the probabili
Solve a Poisson distribution problem #1
I am in SS 3. Give me a Poisson distribution problem where the mean rate of 4 per hour, fi
Solve a Poisson distribution problem #2
I am in SS 3. Give me a Poisson distribution problem where the mean rate of 3 defects per