document.write( "Question 14571: Help me please!
\n" ); document.write( "I don't understand what I am suppose to do.\r
\n" ); document.write( "\n" ); document.write( "Evaluate the determinant of the matrix.\r
\n" ); document.write( "\n" ); document.write( "items in a bracket. 3 -2 0
\n" ); document.write( " -1 5 3
\n" ); document.write( " 2 7 1 \n" ); document.write( "

Algebra.Com's Answer #7314 by glabow(165) $\"\"$ $\"About$

You can put this solution on YOUR website!
The underlying meaning of a determinant is complex and cannot be covered here. It is a useful value to know when working with matrices. There are a couple of ways of calculating the determinant of a matrix, and for a 3 x 3 there is a relatively easy procedure. I'm surpised you haven't been given it (if you haven't) but I'll try it here.
\n" ); document.write( "You first get the products of all the left-to-right diagonals of the matrix and add them up. You then get the products of all the right-to-left diagonals of the matrix and add them up. You then subtract the right-to-left sum from the left-to-right sum. The diagonals are all referenced from top to bottom.
\n" ); document.write( "You can see how this is a very poor way to describe the procedure. Let's make it mathematical.
\n" ); document.write( "We will reference the elements of the matrix with the following notation:
\n" ); document.write( " $\"e%5Bx%2C+y%5D\"$ will mean the element in row x and column y.
\n" ); document.write( "In a 3 x 3 matrix the upper left element will be $\"e%5B1%2C1%5D\"$ and the lower right element will be $\"e%5B3%2C3%5D\"$ . Get it?
\n" ); document.write( "Okay. The left-to-right diagonals are as follows:
\n" ); document.write( " $\"e%5B1%2C1%5D\"$ , $\"e%5B2%2C2%5D\"$ , $\"e%5B3%2C3%5D\"$ ; $\"e%5B1%2C2%5D\"$ , $\"e%5B2%2C3%5D\"$ , $\"e%5B3%2C1%5D\"$ ; and $\"e%5B1%2C3%5D\"$ , $\"e%5B2%2C1%5D\"$ , $\"e%5B3%2C2%5D\"$
\n" ); document.write( "Whew! For the matix values you gave, this amounts to
\n" ); document.write( "(3 x 5 x 1), (-2 x 3 x 2), and (0 x -1 x 7). Do the multiplications and add them up.
\n" ); document.write( "15+(-12)+0 = 3. This is the value of the products of all the left-to-right diagonals.
\n" ); document.write( "The right-to-left diagonals are as follows:
\n" ); document.write( " $\"e%5B1%2C3%5D\"$ , $\"e%5B2%2C2%5D\"$ , $\"e%5B3%2C1%5D\"$ ; $\"e%5B1%2C2%5D\"$ , $\"e%5B2%2C1%5D\"$ , $\"e%5B3%2C3%5D\"$ ; and $\"e%5B3%2C1%5D\"$ , $\"e%5B2%2C3%5D\"$ , $\"e%5B3%2C2%5D\"$
\n" ); document.write( "For the matrix values you gave, this amounts to
\n" ); document.write( "(0 x 5 x 2), (-2 x -1 x 1), and (3 x 3 x 7). Do the multiplications and add them up.
\n" ); document.write( "0+2+63 = 65. This is the value of the products of all the right-to-left diagonals.
\n" ); document.write( "Subtract the right-to-left from the left-to-right.
\n" ); document.write( "Determinant = 3 - 65 = -62
\n" ); document.write( "CHECK MY WORK!!! \n" ); document.write( "

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