{"id":18569,"date":"2022-08-01T12:06:49","date_gmt":"2022-08-01T06:36:49","guid":{"rendered":"https:\/\/apboardsolutions.com\/?p=18569"},"modified":"2022-08-01T14:52:27","modified_gmt":"2022-08-01T09:22:27","slug":"inter-1st-year-maths-1a-chapter-3-ex-3a","status":"publish","type":"post","link":"https:\/\/apboardsolutions.com\/inter-1st-year-maths-1a-chapter-3-ex-3a\/","title":{"rendered":"Inter 1st Year Maths 1A Matrices Solutions Ex 3(a)"},"content":{"rendered":"

Practicing the Intermediate 1st Year Maths 1A Textbook Solutions<\/a> Inter 1st Year Maths 1A Matrices Solutions Exercise 3(a) will help students to clear their doubts quickly.<\/p>\n

Intermediate 1st Year Maths 1A Matrices Solutions Exercise 3(a)<\/h2>\n

I.<\/span><\/p>\n

Question 1.
\nWrite the following as a single matrix.
\n(i) \\(\\left[\\begin{array}{lll}
\n2 & 1 & 3
\n\\end{array}\\right]+\\left[\\begin{array}{lll}
\n1 & 0 & 0
\n\\end{array}\\right]\\)
\n(ii) \\(\\left[\\begin{array}{ccc}
\n3 & 9 & 0 \\\\
\n1 & 8 & -2
\n\\end{array}\\right]+\\left[\\begin{array}{ccc}
\n4 & 0 & 2 \\\\
\n7 & 1 & 4
\n\\end{array}\\right]\\)
\n(iii) \\(\\left[\\begin{array}{c}
\n0 \\\\
\n1 \\\\
\n-1
\n\\end{array}\\right]+\\left[\\begin{array}{l}
\n1 \\\\
\n1 \\\\
\n1
\n\\end{array}\\right]\\)
\n(iv) \\(\\left[\\begin{array}{cc}
\n-1 & 2 \\\\
\n2 & -2 \\\\
\n3 & 1
\n\\end{array}\\right]-\\left[\\begin{array}{cc}
\n0 & 1 \\\\
\n-1 & 0 \\\\
\n-2 & 1
\n\\end{array}\\right]\\)
\nSolution:
\n\"Inter<\/p>\n

Question 2.
\nIf A = \\(\\left[\\begin{array}{cc}
\n-1 & 3 \\\\
\n4 & 2
\n\\end{array}\\right]\\), B = \\(\\left[\\begin{array}{cc}
\n2 & 1 \\\\
\n3 & -5
\n\\end{array}\\right]\\), X = \\(\\left[\\begin{array}{ll}
\nx_{1} & x_{2} \\\\
\nx_{3} & x_{4}
\n\\end{array}\\right]\\) and A + B = X, then find the values of x1<\/sub>, x2<\/sub>, x3<\/sub> and x4<\/sub>.
\nSolution:
\nA + B = X
\n\"Inter
\n\u2234 x1<\/sub> = 1, x2<\/sub> = 4, x3<\/sub> = 7, x4<\/sub> = -3<\/p>\n

\"Inter<\/p>\n

Question 3.
\nIf A = \\(\\left[\\begin{array}{ccc}
\n-1 & -2 & 3 \\\\
\n1 & 2 & 4 \\\\
\n2 & -1 & 3
\n\\end{array}\\right]\\), B = \\(\\left[\\begin{array}{ccc}
\n1 & -2 & 5 \\\\
\n0 & -2 & 2 \\\\
\n1 & 2 & -3
\n\\end{array}\\right]\\) and C = \\(\\left[\\begin{array}{ccc}
\n-2 & 1 & 2 \\\\
\n1 & 1 & 2 \\\\
\n2 & 0 & 1
\n\\end{array}\\right]\\) then find A + B + C.
\nSolution:
\n\"Inter<\/p>\n

Question 4.
\nIf A = \\(\\left[\\begin{array}{ccc}
\n3 & 2 & -1 \\\\
\n2 & -2 & 0 \\\\
\n1 & 3 & 1
\n\\end{array}\\right]\\), B = \\(\\left[\\begin{array}{ccc}
\n-3 & -1 & 0 \\\\
\n2 & 1 & 3 \\\\
\n4 & -1 & 2
\n\\end{array}\\right]\\) and X = A + B then find X.
\nSolution:
\n\"Inter<\/p>\n

Question 5.
\nIf \\(\\left[\\begin{array}{cc}
\nx-3 & 2 y-8 \\\\
\nz+2 & 6
\n\\end{array}\\right]=\\left[\\begin{array}{cc}
\n5 & 2 \\\\
\n-2 & a-4
\n\\end{array}\\right]\\) then find the values of x, y, z and a.
\nSolution:
\nGiven \\(\\left[\\begin{array}{cc}
\nx-3 & 2 y-8 \\\\
\nz+2 & 6
\n\\end{array}\\right]=\\left[\\begin{array}{cc}
\n5 & 2 \\\\
\n-2 & a-4
\n\\end{array}\\right]\\)
\n\u2234 x – 3 = 5 \u21d2 x = 3 + 5 = 8
\n2y – 8 = 2 \u21d2 2y = 8 + 2 = 10 \u21d2 y = 5
\nz + 2 = -2 \u21d2 z = -2 – 2 = -4
\na – 4 = 6 \u21d2 a = 4 + 6 = 10<\/p>\n

II.<\/span><\/p>\n

Question 1.
\nIf \\(\\left[\\begin{array}{ccc}
\nx-1 & 2 & 5-y \\\\
\n0 & z-1 & 7 \\\\
\n1 & 0 & a-5
\n\\end{array}\\right]=\\left[\\begin{array}{ccc}
\n1 & 2 & 3 \\\\
\n0 & 4 & 7 \\\\
\n1 & 0 & 0
\n\\end{array}\\right]\\) then find the values of x, y, z and a.
\nSolution:
\nGiven \\(\\left[\\begin{array}{ccc}
\nx-1 & 2 & 5-y \\\\
\n0 & z-1 & 7 \\\\
\n1 & 0 & a-5
\n\\end{array}\\right]=\\left[\\begin{array}{ccc}
\n1 & 2 & 3 \\\\
\n0 & 4 & 7 \\\\
\n1 & 0 & 0
\n\\end{array}\\right]\\)
\n\u2234 x – 1 = 1 \u21d2 x = 1 + 1 = 2
\n5 – y = 3 \u21d2 y = 5 – 3 = 2
\nz – 1 = 4 \u21d2 z = 4 + 1 = 5
\na – 5 = 0 \u21d2 a = 5<\/p>\n

\"Inter<\/p>\n

Question 2.
\nFind the trace of \\(\\left[\\begin{array}{ccc}
\n1 & 3 & -5 \\\\
\n2 & -1 & 5 \\\\
\n1 & 0 & 1
\n\\end{array}\\right]\\)
\nSolution:
\nTrace of \\(\\left[\\begin{array}{ccc}
\n1 & 3 & -5 \\\\
\n2 & -1 & 5 \\\\
\n1 & 0 & 1
\n\\end{array}\\right]\\) = Sum of the diagonal elements
\n= 1 – 1 + 1
\n= 1<\/p>\n

Question 3.
\nIf A = \\(\\left[\\begin{array}{rrr}
\n0 & 1 & 2 \\\\
\n2 & 3 & 4 \\\\
\n4 & 5 & -6
\n\\end{array}\\right]\\) and B = \\(\\left[\\begin{array}{ccc}
\n-1 & 2 & 3 \\\\
\n0 & 1 & 0 \\\\
\n0 & 0 & -1
\n\\end{array}\\right]\\) find B – A and 4A – 5B.
\nSolution:
\n\"Inter
\n\"Inter<\/p>\n

\"Inter<\/p>\n

Question 4.
\nIf A = \\(\\left[\\begin{array}{lll}
\n1 & 2 & 3 \\\\
\n3 & 2 & 1
\n\\end{array}\\right]\\) and B = \\(\\left[\\begin{array}{lll}
\n3 & 2 & 1 \\\\
\n1 & 2 & 3
\n\\end{array}\\right]\\) find 3B – 2A.
\nSolution:
\n\"Inter<\/p>\n","protected":false},"excerpt":{"rendered":"

Practicing the Intermediate 1st Year Maths 1A Textbook Solutions Inter 1st Year Maths 1A Matrices Solutions Exercise 3(a) will help students to clear their doubts quickly. Intermediate 1st Year Maths 1A Matrices Solutions Exercise 3(a) I. Question 1. Write the following as a single matrix. (i) (ii) (iii) (iv) Solution: Question 2. If A = … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[13],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/18569"}],"collection":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/comments?post=18569"}],"version-history":[{"count":5,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/18569\/revisions"}],"predecessor-version":[{"id":18588,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/18569\/revisions\/18588"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/media?parent=18569"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/categories?post=18569"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/tags?post=18569"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}