(May – 2010)<\/span>
\nAnswer:
\n
\n<\/p>\nQuestion 2.
\n(i) (a) If \\(A=\\left[\\begin{array}{ccc}
\n1 & 1 & 5 \\\\
\n0 & 1 & 3 \\\\
\n0 & -1 & -2
\n\\end{array}\\right]\\)<\/p>\n
What is the value of |3A|?
\n(b) Find the equation of the line joining the points (1,2) and (-3,-2) using determinants.
\n(ii) Show that \\(\\left|\\begin{array}{lll}
\n1 & a & a^{2} \\\\
\n1 & b & b^{2} \\\\
\n1 & c & c^{2}
\n\\end{array}\\right|=(a-b)(b-c)(c-a)\\)
\nAnswer:
\n<\/p>\n
(b) Let (x,y) be the coordinate of any point on The line, then (1,2), (-3, -2) and (x, y) are collinear.<\/p>\n
Hence the area formed will be zero.
\n<\/p>\n
Question 3.
\nConsider the following system of linear equations; x + y + z = 6, x – y + z = 2, 2x + y + z = 1
\n(i) Express this system of equations in the Standard form AXB
\n(ii) Prove that A is non-singular.
\n(iii) Find the value of x, y and z satisfying the above equation. (May – 2011)<\/span>
\nAnswer:
\n<\/p>\n<\/p>\n
Question 4.
\n(i) lf \\(\\left|\\begin{array}{ll}
\nx & 3 \\\\
\n5 & 2
\n\\end{array}\\right|=5\\), then x = ………..
\n(ii) Prove that
\n\\(\\left|\\begin{array}{ccc}
\ny+k & y & y \\\\
\ny & y+k & y \\\\
\ny & y & y+k
\n\\end{array}\\right|=k^{2}(3 y+k)\\)
\n(iii) Solve the following system of linear Equations, using matrix method; 5x + 2y = 3, 3x + 2y = 5 (March – 2012)<\/span>
\nAnswer:
\n
\n<\/p>\nQuestion 5.
\n(i) Let B is a square matrix of order 5, then |kB| is equal to ………..
\n(a) |B|
\n(b) k|B|
\n(c) k5<\/sup>|B|
\n(d) 5|B|<\/p>\n(ii) Prove that \\(\\left|\\begin{array}{lll}
\n1 & x & x^{2} \\\\
\n1 & y & y^{2} \\\\
\n1 & z & z^{2}
\n\\end{array}\\right|=(x-y)(y-z)(z-x)\\)
\n(iii) Check the consistency of the following equations; 2x + 3y + z = 6, x + 2y – z = 2, 7x + y + 2z =10 (May – 2012)<\/span>
\nAnswer:
\n
\n<\/p>\nTherefore the system is consistent and has unique solutions.<\/p>\n
Question 6.
\n(i) Find the values of x in which \\(\\left|\\begin{array}{ll}
\n3 & x \\\\
\nx & 1
\n\\end{array}\\right|=\\left|\\begin{array}{ll}
\n3 & 2 \\\\
\n4 & 1
\n\\end{array}\\right|\\)<\/p>\n
(ii) Using the property of determinants, show that the points A(a,b + c), B(b,c + a), C(c,a + b) are collinear.
\n(iii) Examine the consistency of system of following equations: 5x – 6y + 4z = 15, 7x + y – 3z = 19, 2x + y + 6z = 46 (EDUMATE – 2017; March – 2013)<\/span>
\nAnswer:
\n
\nSince, the system is consistent and has unique solutions.<\/p>\nQuestion 7.
\nConsider a system of linear equations which is given below;
\n\\(\\begin{array}{l}
\n\\frac{2}{x}+\\frac{3}{y}+\\frac{10}{z}=4 ; \\frac{4}{x}-\\frac{6}{y}+\\frac{5}{z}=1 \\\\
\n\\frac{6}{x}+\\frac{9}{y}-\\frac{20}{z}=2
\n\\end{array}\\)<\/p>\n
(i) Express the above equation in the matrix form AX = B.
\n(ii) Find A-1<\/sup>, the inverse of A.
\n(iii) Find x,y and z. (May – 2013)
\nAnswer:
\n<\/p>\nQuestion 8.
\nConsider the matrices \\(A=\\left[\\begin{array}{ll}
\n2 & 3 \\\\
\n4 & 5
\n\\end{array}\\right]\\)<\/p>\n
(i) Find A2<\/sup> – 7A – 21 = 0
\n(ii) Hence find A-1
\n(iii) Solve the following system of equations using matrix method 2x + 3y = 4; 4x + 5y = 6 (March – 2014)<\/span>
\nAnswer:
\n
\n<\/p>\n(iii) The given system of equations can be converted into matrix form AX = B
\n<\/p>\n
Question 9.
\n(i) Let A be a square matrix of order 2 x 2 then |KA| is equal to
\n(a) K|A|
\n(b) K2<\/sup>|A|
\n(c) K3<\/sup>|A|
\n(d) 2K|A|<\/p>\n(ii) Prove that
\n\\(\\left|\\begin{array}{ccc}
\n\\mathbf{a}-\\mathbf{b}-\\mathbf{c} & \\mathbf{2 a} & 2 \\mathbf{a} \\\\
\n2 \\mathrm{~b} & \\mathrm{~b}-\\mathrm{c}-\\mathrm{a} & 2 \\mathrm{~b} \\\\
\n2 \\mathrm{c} & 2 \\mathrm{c} & \\mathrm{c}-\\mathrm{a}-\\mathrm{b}
\n\\end{array}\\right|=(\\mathrm{a}+\\mathrm{b}+\\mathrm{c})^{3}\\)<\/p>\n
(iii) Examine the consistency of the system of Equations. 5x + 3y = 5; 2x + 6y = 8 (May- 2014)<\/span>
\nAnswer:
\n
\n(iii) The given system of equation can be written in matrix form as
\n
\nsolution exist and hence it is consistent.<\/p>\nQuestion 10.
\n(a) Choose the correct statement related to the matnces \\(A=\\left[\\begin{array}{ll}
\n1 & 0 \\\\
\n0 & 1
\n\\end{array}\\right], B=\\left[\\begin{array}{ll}
\n0 & 1 \\\\
\n1 & 0
\n\\end{array}\\right]\\)
\n\\(\\begin{array}{l}
\n\\text { (i) } A^{3}=A, B^{3} \\neq B \\\\
\n\\text { (ii) } A^{3} \\neq A, B^{3}=B \\\\
\n\\text { (iii) } A^{3}=A, B^{3}=B \\\\
\n\\text { (iv) } A^{3} \\neq A, B^{3} \\neq B
\n\\end{array}\\)<\/p>\n
(b) lf \\(M=\\left[\\begin{array}{ll}
\n7 & 5 \\\\
\n2 & 3
\n\\end{array}\\right]\\) then verity the equation M2<\/sup> – 10M + 11 I2<\/sub> = O<\/p>\n(c) Inverse of the matrix \\(\\left[\\begin{array}{lll}
\n0 & 1 & 2 \\\\
\n0 & 1 & 1 \\\\
\n1 & 0 & 2
\n\\end{array}\\right]\\) (March – 2015)
\nAnswer:
\n
\n<\/p>\n
Question 11.
\nSolve the system of Linear equations x + 2y + z = 8; 2x + y – z = 1; x – y + z = 2 (March – 2015)<\/span>
\nAnswer:
\n<\/p>\nQuestion 12.
\n(a) If \\(\\left|\\begin{array}{ll}
\nx & 1 \\\\
\n1 & x
\n\\end{array}\\right|=15\\) then find the value of X.<\/p>\n
(b)Solve the following system of equations 3x – 2y + 3z = ?, 2x + y – z = 1 4x – 3y + 2z = 4 (May – 2015)<\/span>
\nAnswer:
\n
\n<\/p>\nQuestion 13.
\n(i)The value of the determinant \\(\\left|\\begin{array}{ccc}
\n1 & 1 & 1 \\\\
\n1 & -1 & -1 \\\\
\n1 & 1 & -1
\n\\end{array}\\right|\\) is
\n(a) -4
\n(b) 0
\n(c) 1
\n(d) 4<\/p>\n
(ii) Using matrix method, solve the system of linear equations x + y + 2z = 4; 2x – y + 3z = 9; 3x – y – z = 2 (May – 2016)<\/span>
\nAnswer:
\n(i) (d) 4
\n(ii) Express the given equation in the matrix form as AX = B
\n<\/p>\nQuestion 14.
\n(i) If \\(A=\\left[\\begin{array}{ll}
\na & 1 \\\\
\n1 & 0
\n\\end{array}\\right]\\) is such that A2<\/sup> = I then a equals
\n(a) 1
\n(b) -1
\n(c) 0
\n(d) 2<\/p>\n(ii)Solve the system of equations x – y + z = 4; 2x + y – 3z = 0; x + y + z = 2 Using matrix method. (March – 2017)<\/span>
\nAnswer:
\n
\n<\/p>\nQuestion 15.
\n(i) IfA is a 2 x 2 matrix with |A| = 5, then |adjA| is
\n(a) 5
\n(b) 25
\n(c) 1\/5
\n(d) 1\/25<\/p>\n
(ii) Solve the system of equations using matrix method.
\nx + y + z = 1; 2x + 3y – z = 6; x – y + z = -1 (May – 2017)<\/span>
\nAnswer:
\n(i) (a) 5
\n(ii) LetA X=B,
\n
\n<\/p>\nWe hope the Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants help you. If you have any query regarding Kerala Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants are part of\u00a0Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 4 Determinants. Kerala\u00a0Plus Two Maths Chapter Wise Previous\u00a0Questions Chapter 4 Determinants Plus Two Maths Determinants 3 Marks Important Questions Question 1. Prove […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[42728],"tags":[],"yoast_head":"\n
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants - A Plus Topper<\/title>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\t\n\t\n\t\n