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Show that the determinant of the 3x3 matrix (2 1 1 / 2 1 7 / 6 3 5) is equal to zero.

To find the determinant of this matrix, we calculate: 2(1x5-3x7)-1(2x5-6x7)-1(2x3-1x6) = 10 - 42 - 10 + 42 -6 + 6 = 0.So the determinant of this 3x3 matrix is equal to zero.
LG
Answered by LAUREN G. • Maths tutor
4511 Views

Given that y is directly proportional to square root of x and that y = 20 when x = 49 find an expression to represent x and y.

y = k √x20 = k √49 20/7 = ktherefore y = 20/7 √x
AP
Answered by Ann P. • Maths tutor
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Two ordinary fair dice are rolled. Work out the probability that both land on a value less than 4.

The probability of an event= Number of ways an event can occur/ Total number of possible outcomesBoth dices land on values less than 4. This means they both can be 1,2 or 3. Therefore, number of ways the eve...
GS
Answered by George S. • Maths tutor
7199 Views

g(x) = ( x / (x+3) ) + ( 3(2x+1) / (x^2 + x - 6) ). Show that this can be simplified to: g(x) = (x+1) / (x-2).

Step 1: The denominator of the right-hand fraction is quadratic, so we can factorise this to (x+3)(x-2). This looks similar to the denominator of the left-hand fraction, suggesting we can combine the two. St...
AS
Answered by Amar S. • Maths tutor
6281 Views

A curve has the equation: x^2(4+y) - 2y^2 = 0 Find an expression for dy/dx in terms of x and y.

First of all expand the brackets in the equation. Then you can differentiate each term with respect to x. As one of the terms will be a product of x and y the product rule must be used to find the differenti...
CM
Answered by Carlotta M. • Maths tutor
4596 Views