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print(); # input placeholderWe have just included the LinearAlgebra package, which contains all the Matrix commands needed for this assignment.To enter a matrix by hand, QyQ+SSJBRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiM3JDclIiIiIiIjIiIkNyUiIiUiIiYiIidGLg==So a row matrix would be given by QyQ+SSJ1RzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiM3IzclIiIiIiImIiIoRi4=and a column matrix by QyQ+SSJ2RzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiM3JTcjIiIjNyMiIic3IyIjOSIiIg==To generate a random nxn matrix, use the command RandomMatrix(n); QyQ+SSJBRzYiLUktUmFuZG9tTWF0cml4R0YlNiMiIiQiIiI=JSFHTo display the nth column of any matrix A, use the command Column(A, n);QyQtSSdDb2x1bW5HNiI2JEkiQUdGJSIiIkYoSimilarly, to display the nth row of A, use the command Row(A,n);QyQtSSRSb3dHNiI2JEkiQUdGJSIiIkYoNote that the column is displayed as a column vector and the row is displayed as a row vector. To display the (i,j)th entry of a matrix A, enter A[i,j];QyQmSSJBRzYiNiQiIiJGJ0YnMatrix operations such as multiplication and addition can be performed as usual -- use + for addition , use . for matrix multiplication, and * for scalar multiplication.QyQ+SSJCRzYiLUktUmFuZG9tTWF0cml4R0YlNiMiIiQiIiI=QyQsJkkiQUc2IiIiIkkiQkdGJUYmRiY=QyQtSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJIkFHRilJIkJHRikiIiI=QyQ+SSJDRzYiLUktUmFuZG9tTWF0cml4R0YlNiQiIiMiIiQiIiI=QyQtSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJIkNHRilJIkFHRikiIiI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIi5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJDRidGL0YyLUY2Ni1RIjtGJ0Y5RjsvRj9GMUZARkJGREZGRkhGSi9GTlEsMC4yNzc3Nzc4ZW1GJw==%;QyQsJEkiQUc2IiIiJiIiIg==QyQtSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJIkFHRilJInZHRikiIiI=We can also find inverses and determinants for square matrices. The inverse of a matrix A is given by MatrixInverse(A); and the determinant is given by a command we've usedbefore: Determinant(A);QyQ+SSJBRzYiLUktUmFuZG9tTWF0cml4R0YlNiMiIiQiIiI=QyQtSSxEZXRlcm1pbmFudEc2IjYjSSJBR0YlIiIiQyQ+SSJCRzYiLUkuTWF0cml4SW52ZXJzZUdGJTYjSSJBR0YlIiIiQyQtSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJIkFHRilJIkJHRikiIiI=QyQtSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJIkJHRilJIkFHRikiIiI=Elementary row operations such as multiplying a single row by a scalar and replacing a row by that row plus a scalar times another row are both done with the same command, RowOperation. To multiply the ith row in a matrix A by a scalar k, use the command RowOperation(A, i, k); and to replace the ith row with the ith row plus a scalar k times the jth row, use the command RowOperation(A, [i,j],k); Repeated use of this command can put a matrix in echelon form. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEtUm93T3BlcmF0aW9uRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiktRiw2JVEiQUYnRi9GMi1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjY2Ji1GIzYnLUkjbW5HRiQ2JFEiMkYnRkFGPS1GZ242JFEiMUYnRkEvJStleGVjdXRhYmxlR0ZFRkFGQS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9LUkmbWZyYWNHRiQ2KC1GIzYlLUZnbjYkUSMxM0YnRkFGXW9GQS1GIzYlLUZnbjYkUSM1MkYnRkFGXW9GQS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZ3AvJSliZXZlbGxlZEdGRUZdb0ZBRkEtRj42LVEiO0YnRkFGQ0ZGRkhGSkZMRk5GUEZSL0ZWUSwwLjI3Nzc3NzhlbUYnRl1vRkE=JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEtUm93T3BlcmF0aW9uRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiotRiw2JVEiQUYnRi9GMi1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictSSNtbkdGJDYkUSIzRidGQUY9LUY+Ni1RKiZ1bWludXMwO0YnRkFGQy9GR0ZFRkhGSkZMRk5GUC9GU1EsMC4yMjIyMjIyZW1GJy9GVkZbby1JJm1mcmFjR0YkNigtRlk2JFEjMTNGJ0ZBLUYjNiUtRlk2JFElMTI0MkYnRkEvJStleGVjdXRhYmxlR0ZFRkEvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl9wLyUpYmV2ZWxsZWRHRkVGaG9GQUZBLUY+Ni1RIjtGJ0ZBRkNGRkZIRkpGTEZORlBGUi9GVlEsMC4yNzc3Nzc4ZW1GJ0Zob0ZBOf course, Maple can do the whole reduction itself with the command ReducedRowEchelonFormQyRJIkFHNiIiIiI=QyQtSTZSZWR1Y2VkUm93RWNoZWxvbkZvcm1HNiI2I0kiQUdGJSIiIg==QyQ+SSJCRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiM3JTclIiIiIiIjIiIkNyUiIiUiIiYiIic3JUYzIiIoIiIqRi4=QyQtSTZSZWR1Y2VkUm93RWNoZWxvbkZvcm1HNiI2I0kiQkdGJSIiIg==JSFHThe last command you will need for this assignment will find a basis for a homogeneous system of the form Ax=0. Given the matrix A,the command NullSpace(A); will output a basis for the solution space to the homogeneous equation Ax=0. QyQ+SSJBRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiM3JjcmIiM4IiIpIiIoRi83JkYvIiImIiInRjA3JiIjQiIjOSIiKiIjNTcmIiNHIiM8RjgiIzYiIiI=QyQtSTZSZWR1Y2VkUm93RWNoZWxvbkZvcm1HNiI2I0kiQUdGJSIiIg==QyQ+SSJXRzYiLUkqTnVsbFNwYWNlR0YlNiNJIkFHRiUiIiI=QyQmSSJXRzYiNiMiIiJGJw==QyQmSSJXRzYiNiMiIiMiIiI=JSFHTTdSMApJNFJUQUJMRV9TQVZFLzczOTI0NzZYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISMnIiMiJCIiIiIiJSIiIyIiJiIiJCIiJ0YmTTdSMApJNFJUQUJMRV9TQVZFLzI3NDUzMzJYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISMkIiIiJCIiIiIiJiIiKEYmTTdSMApJNVJUQUJMRV9TQVZFLzIxODg0NDQwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQhI1EhI08hI3AiI3AhIzoiIiMhIykpIiMqKiEjZkYmTTdSMApJNFJUQUJMRV9TQVZFLzM0MzU4MjhYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISMqIiQiJCIiKiIjKSkiIyYqIiNqIiM1ISNoISNFISM/ISN5RiY=TTdSMApJNFJUQUJMRV9TQVZFLzI0NDQyMDRYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISMnIiMiJCIiJiIjPyIjNSIjRCIjOiIjSUYmTTdSMApJNVJUQUJMRV9TQVZFLzIxODg0NDQwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQhI1EhI08hI3AiI3AhIzoiIiMhIykpIiMqKiEjZkYm