Algebra We know that matrix multiplication is not commutative: if A and B are square matrices of ...
Algebra We know that matrix multiplication is not commutative: if A and B are square matrices of the same size, AB and BA are usually different We say that A and B commute if it so happens that AB BA. Determine all numbers a, b, e, d, such that the matrix com- mutes with both Calculus An object with mass m is dragged along a horizontal plane by a force acting along a rope attached to the object as shown below. mass horizontal plane If the rope makes an angle θ with the plane, then the magnitude of the force required to overcome friction is umg where g is the acceleration due to gravity and u is a positive constant called the ooeficient offriction, and we assume θ E [O,T/2) Use the second derivative test to show that F is minimised when Hint: all of the constants μ, m and g are positive.
Algebra We know that matrix multiplication is not commutative: if A and B are square matrices of the same size, AB and BA are usually different We say that A and B commute if it so happens that AB BA. Determine all numbers a, b, e, d, such that the matrix com- mutes with both Calculus An object with mass m is dragged along a horizontal plane by a force acting along a rope attached to the object as shown below. mass horizontal plane If the rope makes an angle θ with the plane, then the magnitude of the force required to overcome friction is umg where g is the acceleration due to gravity and u is a positive constant called the ooeficient offriction, and we assume θ E [O,T/2) Use the second derivative test to show that F is minimised when Hint: all of the constants μ, m and g are positive.