1,332 prompts matching "Explain solving cubic equations back to me"
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Explain pre-multiplication and post-multiplication
I keep mixing up pre-multiplying and post-multiplying matrices. Use two 2x2 matrices A and
Identify symmetric matrices practice
Give me three different 3x3 matrices and ask me to test each one for symmetry using A = A^
Explain the identity matrix
Explain what the identity matrix I is and show, with a 3x3 numerical example, that AI = IA
Explain the zero matrix in matrix algebra
I am in SS 3. Explain the zero matrix and its effect in addition, using a 2x2 example to s
Explain the rule of signs for determinants
Explain the checkerboard pattern of positive and negative signs used when expanding a 3x3
Explain the adjoint of a matrix
Explain what the adjoint of a matrix is and how it relates to the matrix of cofactors, usi
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
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 particle and rigid body in mechanics
Ask me to explain the difference between a particle and a rigid body in mechanics, with an
Explain the parallelogram of forces
Explain the parallelogram law for finding the resultant of two forces, with a labelled dia
Explain the conditions for equilibrium of a rigid body
I am in SS 3. Explain the principal conditions needed for a rigid body to be in equilibriu
Explain the polygon of forces
I am in SS 3. Explain what the polygon of forces method is and how it shows several concur
Explain friction and the coefficient of friction
I am in SS 3. Explain what friction force is, how the coefficient of friction relates to t
Solve a quadratic equation with complex roots #1
I am in SS 3. Give me a quadratic equation problem where I need to solve x^2 + 4 = 0 for c
Solve a quadratic equation with complex roots #2
I am in SS 3. Give me a quadratic equation problem where I need to solve x^2 - 2x + 5 = 0
Solve a quadratic equation with complex roots #3
I am in SS 3. Give me a quadratic equation problem where I need to solve 2x^2 + x + 3 = 0
Explain equal complex numbers
I am in SS 3. Explain the condition for two complex numbers to be equal (real parts equal
Explain finding area under a curve using integration
I am in SS 3. Explain how definite integration gives the area under a curve between two li