Synergy Linear algebra Answers to 100 questions tests

Synergy of MFPU MY. Linear algebra. Answers to 100 questions. Excellent 1. Specify the natural sequence of numbers •1, 2, 3, 4, 5, 6, 7, 8, 9, ... •1, 0, 1, 2, 3, 4, 5, 6, 7, 8 , 9, ...?2, ?3, ?4, ?5, ?6, ?7, ?8, ?9, ?..., •-1, -2, -3, -4, -5 , -6, -7, -8, -9 •0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ... 2. Vectors are called coplanar if •they lie in the same plane • they are perpendicular to the same plane •they lie in the same plane or on parallel planes 3. Using the Cramer method (determinants) you can find the solution 4. Calculate the determinant •56 •42? •1 •0 5. Calculate the determinant •3 •6 •22 •18 6. Which of the following numbers is irrational? •1/2 •5.4(15) •3.141592... •4.99 7. Given: Find •32 •40 •10 •20? 8. How many integers satisfy the inequality -8; 4? •9 •12 •13 •11 •10 9. Which of the following vectors is collinear with the vector ? • • • • 10. Find the angle between the vectors a = 2m 4n and b = m - n, where m and n are unit vectors and the angle between m and n is 120° •180 •100 •120 •90 11. What numbers are called whole? •only positive numbers •only natural numbers and numbers opposite to natural numbers •natural numbers, numbers opposite to natural numbers, and number •only numbers ending in 12. For what value of l are the vectors and collinear if M(-3; 2), P (-1; -2) K(2; 1), D(5; l)? •-4.5 •-5 •-4 • 13. Simplify the expression • • • • 14. Simplify the irrational expression • • •-22 •22 15. Find the value of the expression when a = 2 •2 • •1 • 16. Find general solution of the system • • • • 17. Calculate • • • • 18. Given points M(-5; 7; -6), N (7; -9; 9). Calculate the projection of the vector onto the vector •25 •4 •75 •3 19. The vectors and serve as diagonals of the parallelogram ABCD. Express the vector in terms of vectors and • • • 20. Find the value of the expression • • • • 21. Which vectors are called collinear? •lying on the same line or on parallel lines 22. Calculate the determinant 23. Given: Calculate •144 •11 •13 •12 24. Calculate the expression •10000 •1000 •100 •10 25. Which of the following fractions is a mixed periodic fraction? •7,(3) •3.14 •8,(11) •2.75(12) 26. Find •- 2 or 2 •- 2 •2 27. Find l if • •3 •3 or -3 • 28. Vectors and are mutually perpendicular (orthogonal), and and . Define •17 •8.5 •7 •13 29. What is the scalar product of two vectors? 30. Find l if 31. Calculate to the nearest tenth 32. Given vectors and Find the projection of the vector onto the vector axis 33. A system of linear equations is called definite if 34. Establish the relative positions of the lines and 35. Find the acute angle between the lines and ° 36. Determine the equation of the straight line cutting off the segment b = 2 on the Oy axis and making an angle j = 45° with the Ox axis 37. Find the equation of the straight line passing through the intersection point of the lines 2x 3y - 8 = and x - 4y 5 = and through the point M1 (-2; 3) 38. Write the canonical equation of a hyperbola whose foci lie on the Ox axis, if given a = 6 and b = 2 39. Write the equation of a circle that passes through the point A (3; 1), and its center lies on the straight line 3x-y-2 = 40. equation of a plane, knowing that point A(1,-1,3) serves as the base of a perpendicular drawn from the origin to this plane 41. Determine the eccentricity of an equilateral hyperbola 42. State the equation of a circle that passes through point A(2,6) and its center coincides with point C(-1; 2) 43. Write the canonical equation of an ellipse if its semi-axes a= 5 and b= 4 are given 44. Write the equation of a circle of radius R= 8 with center at point C(2;-5) 45. Specify the canonical equations of the straight line 46. Specify the canonical equation of the ellipse, the distance between the foci of which is equal to

75. The matrix equation A * X = B has a solution 76. Find A  B, where ; 77. Find the inverse matrix for matrix 78. Solve the matrix equation AX AXA = B, where ; . 79. Expand the determinant 80. Indicate the equation of a circle whose center coincides with the origin, and the straight line 3x-4y 20=0 is tangent to the circle 81. At what positive value of the parameter t are the straight lines given by the equations 3tx-8y 1=0 and (1 t)x-2ty=0, parallel? 82. Given the vertices of triangle ABC: A(3; -1), B(4; 2) and C(-2; 0). Write the equations of its sides 83. Find the coordinates of the point K of intersection of the line with the plane 2x 5y- 3z= 0 84. Write the equation of the circle passing through the point (4; 5) with the center at the point (1; -3) 85. Find the coordinates of the point of intersection straight lines 2x-y- 3 = 0 and 4x 3y- 11 = 0 86. Find the equation of the line passing through the points M1(3; 2), M2(4;-1) 87. Convert the equation 3x - 4y 12 = 0 to the equation in segments 88. Determine the semi-axes of the hyperbola 89. Indicate the equation of a circle for which points A(3; 2) and B(-1; 6) are the ends of one of the diameters 90. Indicate the equation of a parabola with vertex at point O and focus F(4 ;0) 91. Determine the semi-axes of the hyperbola 25x2 - 16y2 = 1 92. Given straight lines and At what value of α are they perpendicular? 93. Write an equation for a plane passing through parallel lines and 94. For what positive value of the parameter t are the lines given by the equations 3tx - 8y 1 = 0 and (1 t) x - 2ty = 0 parallel? 95. Which of the following numbers is irrational? 96. The determinant of a system of three linear inhomogeneous equations with three unknowns is equal to 5. This means that 97. Give the equation of a circle that passes through the point A(3;1), and its center lies on the line 3x-y- 2 = 0 98. Determine the equation of the plane, knowing that point A(1,-1,3) serves as the base of a perpendicular drawn from the origin to this plane 99. Determine the eccentricity of the equilateral hyperbola 100. Determine the equation of the circle that passes through point A(2;6) and its center coincides with point C(-1; 2)

Synergy Linear algebra Answers to 100 test questions. This is a study guide that contains answers to 100 questions on linear algebra. The manual presents tests consisting of tasks and questions of varying complexity that will help test knowledge on this topic. The manual also contains detailed solutions to problems and explanations of theoretical issues. This material may be useful for students studying linear algebra in universities and colleges, as well as for schoolchildren preparing to enter universities.

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Synergy Linear Algebra is a study guide that contains answers to 100 questions and tests on linear algebra. This is a resource to help students deepen their knowledge of linear algebra and prepare for exams. The manual contains both theoretical materials and practical tasks that will help consolidate the acquired knowledge. The manual is written in Russian and can be used as additional material for textbooks on linear algebra. It is intended for higher education students and anyone interested in mathematics and its applications. With this manual, you can master the basic concepts and methods of linear algebra and test your knowledge with test questions.

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