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How can you prove that similar matrices have the same trace?
you tell me
What is the relationship between x and y in a non-linear graph?
I believe one of the relationships between x and y in a non-linear graph will be the slope of each point will be unproportional. Therefore, it will create a non-straight line (usually a curved line) on the graph. If it's a linear graph, the slope is proportional and the line will be straight. If anyone thinks this is not "straight to the point", please feel free to correct this.{Added}. You are correct! The non-linear trace is curved. Linear means the trace is a straight line, produced when the y values are controlled by straightforwardly multiplying each x value by a constant which can be any number (except of course, 0).A non-linear graph is one in which the y ordinates are controlled by x^N where N is not equal to 1, by a trigonometrical or logarithmic function of x; or in the particular case of the Hyperbola, the reciprocals of the x values.What happens though in y = x^N when N does = 0? I'll leave it to you to spot the result - you don't need to calculate or plot it to realise the answer!
How can i draw a venn diagram of 10 subsets?
One way is to use coins and trace 10 circles which may or may not overlap depending on the intersections of your sets. It does get messy with lots of them. Some people use rectangles instead since they are easier to draw when you have so many.
How do you rotate a triangle 90 degrees about a point?
Trace the triangle on tracing paper, flip the tracing paper so the drawn triangle is touching the paper and then put your pencil on the point (with the tracing paper underneath) that you need to rotate from. Then rotate the paper 90 degrees and draw over the triangle you drew on the tracing paper to stamp it down.
To find discriminant of a matrix?
Well, Im not sure if this is true for all matrices of all sizes, but for a 2x2 square matrix the discriminant is... dis(A) = tr(A)^2 - 4 det(A) The discriminant of matrix A is equal to the square of the trace of matrix A, minus four times the determinant of matrix A. I know this to be true for all 2x2 square matrice, but I have never seen any statement one way or the other for larger matrices. Thus, for matrix A = [ a, b; c, d ] tr(A) = a+d det(A) = ad-bc tr(A)^2 = a^2 + 2ad + d^2 4 det(A) = 4ad - 4bc dis(A) = a^2 - 2ad + 4bc + d^2
