25. (a) Find all2 x 2 matrices whose null space is the line 3x 5y 0...
(1 point) Find a basis for the column space of 0 A = -1 2 3 3 - 1 2 0 - 1 -4 0 2 Basis = (1 point) Find the dimensions of the following vector spaces. (a) The vector space RS 25x4 (b) The vector space R? (c) The vector space of 6 x 6 matrices with trace 0 (d) The vector space of all diagonal 6 x 6 matrices (e) The vector space P3[x] of polynomials with...
4. Classify the null space of each of the following matrices as either a line or a plane: [1 2 3] [1 0 1 0] A= 0 0 2 B= 0 1 0 1 Lo o 1] LO 0 0 0 0 0 1] _ 0 -1 1]
For the following linear system: 2x--3x +5x2-7x4-0 X-2x+3x-2xs-0 3x3-3 x-x-3x: 0 X:+8 x 9 x3+11 xs-0 (1) Represent this linear system in the form Ax = b. (ii) Explain what the null space of the coefficient matrix A is in terms of the linear system (ii) Find a basis for the null space of A. (iv) Find the rank and nullity of matrix A.
SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY THE CRAMER'S METHOD 3X+5Y+3Z-12 2X+5Y-2Z-6 3x+6Y+3Z-3 a) X Y b) CHECK YOUR RESULTS. (USE MATRICE FUNCTIONS, PRESS F2. AND THEN PRESS CTRL+SHIFT+ENTER) 3IF Y-SINC) EXPOO. INTEGRATE Y FROM X-0 Tox-1. COMPARE WITH REAL VALUE IF DX-0 a) INT b) INT ,IF DX- 005 REAL VALUE 3) Plot sin x letting maco c/ Prepave hese cuves 4) SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY INVERSE METHOD 3 X+3Z-13 2X +5 Y-2Z-2 3 X+6Y+2Z-3 Z-...
Find the x-intercept and the y-intercept of each equation. 33. - 3x + 2 y = 12 34 34. 2x – 3y = 24 CHAP FUN Find the slope of the line through each pair of points. 36. (-8, 6) and (-8,-1) In ma relati types an ir 35. (-12, 3) and (-12, -7) 37. (6, -5) and (-12,-5) Find the slope of each line. 38. 3x – 2y = 3 40. x = 6 39. y = 5x +12...
1. Find a basis for the null space and row space of 1-13 (a) A 5-4 -4 7 -6 2 2 0 3 (b) A544 7 -6 2 1. Find a basis for the null space and row space of 1-13 (a) A 5-4 -4 7 -6 2 2 0 3 (b) A544 7 -6 2
Q5. Assume that the following two matrices are row equivalent: A= -2 4 -2 4 2 -6 -3 -3 8 2 -3 1 B= 1 0 6 - 7 0 2 5 - 5 0 0 0 -4 Find bases for the column space and null space of A.
Let M4x3 be the vector space of all 4 x 3 matrices with real entries. Note that M4x3 R12 (M4x3 is isomorphic to R12). Let Z4x3 = {A E M4x3 | all row and column sums of Z are zero}. For example, A= -5 3 2 1 -3 2 1 2 -3 3 -2 -1 is an element of Z4x3. (a) Find a 7 x 12 matrix C whose null space is isomorphic to Z4x3. In other words, find a...
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x, y, z] = [2,-2, 0] + r[2 kx+Zy-4: = 12. -3] is parallel to the plane (2 marks) 24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x,...
Problem 5 (25 points). Let Mat2x2(R) be the vector space of 2 x 2 matrices with real entries. Recall that (1 0.0 1.000.00 "100'00' (1 001) is the standard basis of Mat2x2(R). Define a transformation T : Mat2x2(R) + R2 by the rule la-36 c+ 3d - (1) (5 points) Show that T is linear. (2) (5 points) Compute the matrix of T with respect to the standard basis in Mat2x2 (R) and R”. Show your work. An answer with...