Does the following matrix A = (2 2 // 3 9) (upper row then lower row) have an inverse? If the matrix A^2 is applied as a transformation to a triangle T, by what factor will the area of the triangle change under the transformation?

The answer to the first part is that the matrix does have an inverse. This is found by finding the determinant of the matrix from the formula ad - bc (for some matrix ( a b // c d ) ) to get the answer 29 - 23 = 12. Since this is not equal to zero, the matrix has an inverse. For the second part, we know that the multiple of two matrices will have determinant equal to the product of the determinants of the two matrices, in this case 12*12 = 144 (Also allow direct computation of A^2 with matrix multiplication). The determinant is the factor by which the area of a shape will change under the transformation, so the area of triangle T will change by factor 144.

CO
Answered by Calum O. Further Mathematics tutor

2702 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Take quadratic equation x^2-6x+14=0 and its solutions a and b. What is a/b+b/a?


Find the vector equation of the line of intersection of the planes 2x+y-z=4 and 3x+5y+2z=13.


Whats the derivative of sin(3x)?


If the complex number z = 5 + 4i, work out 1/z.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning