28/03/2020 Matrices and Transformation(Senior Class Maths Study by Topics) 28/03/2020 0Comments by Gate Academy Welcome to your Matrices and Transformation(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. Find the value of b² + c² + d² a² - b² - c² - d² c² + d² a² + b² + c² + d² 2. If x, y, z are the 10th, 13th and 15th terms of a G.P. find the value of 2 1 3 0 3. Find the value of x such that the points (0, 2), (1, x), and (3, 1) are collinear 5/3 3/5 2/5 5/2 4. Solve the equations: x + 2y - z = 4 2x + 3y - z = 2 -x + y + 3z = -1 x = 6, y = 2, z = -15 x = 2, y = -3, z = 8 x = -5, y = 6, z = 10 x = 3, y = -4, z = 9 5. Given that A =find A33 7 -2 4 5 6. What is the image of the point (2, 3) under the mapping : x → 2x + y y → x - y (2, -3) (7, -1) (3, 2) (1, 7) 7. Factorize completely xy(y + x)((y + x) xy(y - x)(y + x) x(y - x)y(y + x) xy(x -y)(x + y) 8. Given that I is a (2x2) unit matrix and Determine the constant k and m such that A² = kA + mI k =-5, m = -4 k = 2, m = -5 k = 4, m = 4 k = 4, m = -5 9. What type of transformation is shown by the matrix ? rotation reflection translation enlargement 10. The matrices A and B are given by: A =and B =where a ≠ 0, b ≠ 0If BA =kA, where k is a scalar, Find another equation satisfied by a and b a + 3b = 0 3a + kb =1 2a + 5b = 3 2a + (1 - k)b = 0 11. Evaluate the determinant 10 12 -14 14 12. The image of the point P under a translation by the vectoris (-2, -1). Find the coordinates of P. (3,5) (-2,4) (4,7) (7, -4) 13. If , what is |A| 2 0 1 -1 14. Two matrices P and Q are given by P = (x, y), Q =where x ≠ 0, y ≠ 0.Given that PQ =λP, where λ is a scalar, obtain the roots of the equation inλ² -6λ + 5 = 0 1 or 5 1 or -5 2 or 7 -3 or 5 15. Find the determinant of the matrix 3 4.2 4 5 16. Find the minor of a23 in -6 -3 -5 -4 17. Determine the order of the matrix 3x3 1x2 2x4 3x4 18. Given that A =find A32 2 7 -2 4 19. A mapping of plane into itself takes the line 3x + 2y = 6 onto the line 2y = 3x + 6. What is the mapping? Reflection on the y-axis Rotation on the y-axis Rotation on the x-axis Reflection on the x-axis 20. Which is the best description for the transformation given by the following matrix, reflection in y-axis reflection in y = x reflection in x-axis reflection in y = -x 21. Find the image of the points under a rotation through 90° in the anticlockwise sense about the origin A(3, 2) (1, 3) (-2, 3) (-3, 2) (3, 2) 22. If , find x -13 14 -11 12 23. Which type of matrix shows a translation? 2x2 1x3 1x2 2x1 24. Find the image of the points under a rotation through 90° in the anticlockwise sense about the origin D(1, -2) (2, 1) (1, -2) (-1, -2) (-1, 2) 25. If A = 2B where A and B are square matrices of the order 3 x 3 and |B|= 5, what is |A|? 45 54 40 50 1 out of 25 Time is Up! Time's up