Math-Exercises.com - Math exercises with correct answers. Transformation of axes 3. 0 A matrix Afor which Ap= 0 n, where pis a positive integer, is called nilpotent. A)-12 -6 25 9 B) 3 -90 0025 C) AB is undefined. Find the inverse of the Matrix: 41 A 32 ªº «» ¬¼ Method 1: Gauss – Jordan method Step1: Set up the given matrix with the identity matrix as the form of 4 1 1 0 3 2 0 1 ªº «» ¬¼ Step 2: Transforming the left Matrix into the identical matrix … Write the system, the matrix equations, and solve: Finding the Numbers Word Problem… Answers to Odd-Numbered Exercises14 Chapter 3. A�+Q�����y�q��!g��u� Zo��=�xS�G+.hn@��4=��������$[!�A� @@�j��t8[rxg=V?�AQn�j��^;��"q޼�����q���`��Nsi3�mi�,�gV0$�[7�+��rO��a��k%-"���W(ܭ4�|�-��O6s�DS��y,b�����4��e�ş�DE��]���f��ߕ��� �I�Q�-_L&e��.+~���'�`�)X��Z^d_�-��R��Rޮ�u�S�5���;�˓��ѷ�x̖�B�HJ(������JMڕ���N�V��{��KI�!P�S��#ㄼ>�if��7�C9���Za��?UVI�"sN����_�W�,�*1�Ѣ�w�x��)�����=���#�3gZ�o`����S�S]�w�yy�]y�벹EjE���I^3���$�`� �f��ax[mCV�ٝ.z2a�� wm����!dl�٘i��Vq7G،��n���%��m�?,#��a���,-�=�)V�p�]?.�|Z���ԁ�!lY�u�]�78�6 ��� M=�o��"��擉��Z�JM����v�������D-�um�,�%�>�ɺ���ʿ���s ��r *�_Y��}��Sl�")�:�*�U�N�jj�cmg"�5���h��g����/n��a��F;b��"U�*�Q�d���ssa zr�#v�߶�?Zw|��J���"���d��lVG8���Rx�����:\�&�[n�Z� \^p�Q���d@�6�M�i� endstream endobj 155 0 obj 797 endobj 127 0 obj << /Type /Page /Parent 118 0 R /Resources 128 0 R /Contents 143 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 128 0 obj << /ProcSet [ /PDF /Text ] /Font << /F3 132 0 R /F4 133 0 R /F6 136 0 R /F8 134 0 R /F13 129 0 R /F14 131 0 R /F16 146 0 R /F18 144 0 R /F19 148 0 R /F20 147 0 R /F21 149 0 R /T10 139 0 R >> /ExtGState << /GS1 151 0 R /GS2 150 0 R >> >> endobj 129 0 obj << /Type /Font /Subtype /Type1 /Name /F13 /Encoding 130 0 R /BaseFont /Times-Roman >> endobj 130 0 obj << /Type /Encoding /Differences [ 128 /Adieresis /Aring /Ccedilla /Eacute /Ntilde /Odieresis /Udieresis /aacute /agrave /acircumflex /adieresis /atilde /aring /ccedilla /eacute /egrave /ecircumflex /edieresis /iacute /igrave /icircumflex /idieresis /ntilde /oacute /ograve /ocircumflex /odieresis /otilde /uacute /ugrave /ucircumflex /udieresis 176 /brokenbar 180 /twosuperior /threesuperior 188 /onequarter 190 /threequarters 192 /Agrave 201 /onehalf 204 /Igrave 209 /Egrave /Ograve /Oacute /Ocircumflex /Otilde 215 /Ydieresis /ydieresis /Ugrave /Uacute /Ucircumflex 221 /Yacute /thorn 228 /Atilde /Acircumflex /Ecircumflex /Aacute 236 /Icircumflex /Iacute /Edieresis /Idieresis 253 /yacute /Thorn ] >> endobj 131 0 obj << /Type /Font /Subtype /Type1 /Name /F14 /BaseFont /Symbol >> endobj 132 0 obj << /Type /Font /Subtype /Type1 /Name /F3 /Encoding 142 0 R /BaseFont /Helvetica >> endobj 133 0 obj << /Type /Font /Subtype /Type1 /Name /F4 /Encoding 142 0 R /BaseFont /Times-Roman >> endobj 134 0 obj << /Type /Font /Subtype /Type1 /Name /F8 /FirstChar 32 /LastChar 255 /Widths [ 250 333 333 500 500 833 667 250 333 333 500 500 333 333 333 278 500 500 500 500 500 500 500 500 500 500 278 278 500 500 500 500 833 556 556 556 611 500 500 611 611 278 444 556 500 778 611 611 556 611 611 556 500 611 556 833 556 556 500 333 250 333 500 500 333 500 500 444 500 500 278 500 500 278 278 444 278 778 500 500 500 500 333 444 278 500 444 667 444 444 389 274 250 274 500 250 556 556 556 500 611 611 611 500 500 500 500 500 500 444 500 500 500 500 278 278 278 278 500 500 500 500 500 500 500 500 500 500 500 400 500 500 500 420 550 500 830 830 860 333 333 0 778 611 0 500 0 0 500 500 0 0 0 0 0 300 300 0 722 500 500 333 500 0 500 0 0 500 500 1000 0 556 556 611 833 722 500 1000 500 500 278 278 500 0 444 556 167 500 278 278 500 500 500 333 278 500 1111 556 500 556 500 500 278 278 278 278 611 611 0 611 611 611 611 278 333 333 333 333 333 333 333 333 333 333 ] /Encoding 142 0 R /BaseFont /NMLKMF+Helvetica-Condensed-Bold /FontDescriptor 135 0 R >> endobj 135 0 obj << /Type /FontDescriptor /Ascent 750 /CapHeight 750 /Descent -189 /Flags 262176 /FontBBox [ -169 -250 1091 991 ] /FontName /NMLKMF+Helvetica-Condensed-Bold /ItalicAngle 0 /StemV 130 /XHeight 564 /CharSet (���o�0���F\r���f0ǵ2Cxt�_���t¡?�8��-�uQ�Q�ߗ�]�Q|���/^g�j�\)jo \ -&��[��Gb:f�i,ڒED��`��������3�c������k\n�ن�b��) /FontFile3 152 0 R >> endobj 136 0 obj << /Type /Font /Subtype /Type1 /Name /F6 /Encoding 142 0 R /BaseFont /Helvetica-Bold >> endobj 137 0 obj << /ProcSet [ /PDF ] >> endobj 138 0 obj << /Type /Encoding /Differences [ 32 /space ] >> endobj 139 0 obj << /Name /T10 /Type /Font /Subtype /Type3 /Resources 137 0 R /FontBBox [ 209 459 211 461 ] /FontMatrix [ 0.001 0 0 0.001 0 0 ] /FirstChar 32 /LastChar 32 /Encoding 138 0 R /CharProcs 141 0 R /Widths [ 310 ] >> endobj 140 0 obj << /Length 51 /Filter /FlateDecode >> stream Part 1: Fred was hired at the ice-cream store, open Friday, Saturday, and Sunday, to help keep track of their sales. Matrices in Mathematics Questions and Answers Test your understanding with practice problems and step-by-step solutions. Background 25 4.2. Dunn 4 . An upper triangular matrix is a square matrix with all its elements below the main diagonal equal to zero. Chapter 9 Matrices and Transformations 239 The answers to the questions in the activity below should help you discover a number of important points relating the matrix arithmetic and algebra. 1.1 Linear Equations and Solutions Suppose we have a system of r linear equations in s unknown variables.