Find the values of x, y, z and w in the following matrix equation

.

By using the matrix method, find the image of the point (3, -2) after a reflection in the line y= -x followed by another reflection in the line x=0

The inverse of matrix A is  

Find matrix A. 

Amani and Asha bought Coca-cola and Pepsi drinks for a farewell party. Amani spent Tshs. 9950 to buy 12 bottles of Coca-cola and 5 bottles of Pepsi drinks. Asha spent Tshs. 8150 to buy 9 bottles of Coca-cola and 5 bottles of Pepsi drinks. Formulate a system of linear equations and hence apply the matrix method to find the price of one bottle of each type of the drinks.

Point A(4, 2) is reflected in the line y + x = 0 followed by an anticlockwise rotation through 90^° about the origin. Find the final image of point A.

 Given the matrices .

Find  

If the matrix  is singular, find the possible value of k

Solve the following system of linear equations by using inverse matrix method

Find the inverse and identity matrix of A = .

A linear translation Q carried point (x,y) into (x?,y?) such that x? = 5 ? 3x y and y? =? 2 + 4x y
(i) Determine the transformation matrix Q.

(ii)  Find Q(3,3)

(iii)  Find the image of the point obtained in part (b)(ii) under Q.

 Given matrices

And

Such that

Find elements of matrix P

Given a triangle with vertices A(0,0) , B(3,0) and C(3,1) ? find its image under:

(i)  a translation by the vector (2,3),

(ii)  the enlargement matrix

(d)  Sketch the triangle and the images in parts (c)(i) and (ii) on the same pair of axes and comment on their sizes.

The matrices 

      and             

are such that AB=A + B.

Find the values of a, b, c and d

Triangle PQR vertices at P(2, 2), Q(5, 3) and R(4, 1) is mapped onto triangle P'Q'R' by transformation matrix 

Find coordinate of triangle P'Q'R'

Determine the values of x which the matrix below has no inverse

The matrices 

      and             

are such that AB=A + B.

Find the values of a, b, c and d

Triangle PQR vertices at P(2, 2), Q(5, 3) and R(4, 1) is mapped onto triangle P'Q'R' by transformation matrix 

Find coordinate of triangle P'Q'R'

Determine the values of x which the matrix below has no inverse

Find the image of the point A(4, 2) after a rotation about the origin through 120⁰ anticlockwise.

Solve the following system of simultaneous equations by using the matrix method.

Triangle ABC has the vertices A (l , l ), B (2, 4) and C (5, 3). Find the vertices of its image under the transformation matrix

If matrix A is singular, what will be the value of y given that

Solve the following simultaneous equation by matrix method

2x + y = 7

4x+3y = 17

Find the image of (3, 5) after rotation of 270^o about the origin in anticlockwise direction.

Find the value of t given that;

 is a singular matrix

Find the image of a line x − 10y = 7, when undergoes reflection at the line x = y then translated at a factor T = (−2, 2)

(i) If 

find |A| and A^?1.

(ii) Use the inverse matrix obtained in (i) to solve 3x + 2y = 12 and 4x ? y = 5.

(i) Determine a matrix M which represents a reflection in the line y ? x = 0

(ii) Find the image of the line x + 2y ? 4 = 0 after a reflection in the line y ? x = 0.

(a) Given

find A^?1.

(b) Use the results obtained in part (a) to find the point of intersection of the following system of simultaneous equations:

2x + 6y = 22

4x + 8y = 32

(c) Find the image of the point obtained in part (b) above under a rotation 90° anticlockwise.

Solve the following simultaneous equations by matrix method.

The vertices of ABC are A(1,2) , B(3,1) and C(? 2,1). If triangle ABC is reflected on the x­axis, find the coordinates of the vertices of its image.

Find the value of k such that the matrix is singular.

It is given that and k is a real number.

(i) Find the matrix A ? kI

(ii) Show that the matrix in c(i) above has no inverse if k² ? 3k ? 10 = 0

Find the enlargement matrix which maps the point (? 3,4) into (18,? 24).

Reflect the point (1,2)in the line x + y = 0.

For what values of n will the matrix 

be non-singular? (10 marks)

A transformation T has the matrix 

Under the same transformation T, the point (-4, 1) is mapped onto the point (6, 3). Find x and r.