What would happen to this problem if there weren’t parentheses?

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Presentation transcript:

What would happen to this problem if there weren’t parentheses? Warm Up Solve for x and y: What would happen to this problem if there weren’t parentheses? **Watch your signs**

Determinants & Inverses

A real number associated with any square matrix A, denoted by Determinants A real number associated with any square matrix A, denoted by detA or |A|

Determinant of a 2x2 - cb = ad

Ex. Evaluate the determinant: =1(7) — 2(4) = 7 - 8 = -1

Ex. Evaluate the determinant: =7(3) - 2(-2) = 21 + 4 = 25

What can I add to a matrix by to keep it the same? What is an ADDITIVE….. IDENTITY: What can I add to a matrix by to keep it the same?

What can I add to a matrix to eliminate all elements? What is an ADDITIVE….. INVERSE: What can I add to a matrix to eliminate all elements?

What is a MULTIPLICATIVE….. IDENTITY: What can I multiply a matrix by to keep it the same? ***We call this the IDENTITY matrix***

What is a MULTIPLICATIVE….. INVERSE: What can I multiply a matrix by to get the Identity Matrix? *** Multiplicative Inverse = ***

How do I actually find the Inverse Matrix? You need to find the determinant!!!

The Inverse of a 2x2 Matrix ***If ad-cb=0, then the matrix has no inverse!!!! A-1= As long as ad-cb =0

Ex. Find A-1, if it exists. A-1=

Ex. Find A-1, if it exists. A-1=

A-1= Does not exist, because it’s not a square matrix! Ex. Find A-1, if it exists. NOT POSSIBLE A-1= Does not exist, because it’s not a square matrix!

Homework: ***Worksheet*** 1.3