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Warm-Up

Warm-Up. 1. Evaluate whether is equal to 2. Solve the matrix equation for x and y 3. Solve the matrix equation for x and y. Day 10 – Determinants and Inverses. SWBAT to find the determinants and inverse of a 2x2 matrix. SWBAT to find the inverse of a 3x3 matrix.

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Warm-Up

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  1. Warm-Up 1. Evaluate whether is equal to 2. Solve the matrix equation for x and y 3. Solve the matrix equation for x and y

  2. Day 10 – Determinants and Inverses SWBAT to find the determinants and inverse of a 2x2 matrix. SWBAT to find the inverse of a 3x3 matrix.

  3. Determinants • determinants • A real number associated with any square matrix A • Denoted by detA or |A|

  4. Determinant of a 2x2 = ad - cb

  5. Evaluate the following determinants - (-t)(-r) =qs-tr qs (-e)(-h) = eh -gf - (g)(f)

  6. Evaluate the following determinants

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

  8. What is a MULTIPLICATIVE Inverse? What can I multiply a matrix by to get the Identity Matrix? Multiplicative INVERSE = A-1

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

  10. Inverse of a 2x2 Matrix NOTICE: a and d switch places while b and c change signs! As long as ad-cb ≠ 0 If ad-cb = 0, then the matrix does not have an inverse!

  11. Find A-1, if it exists.

  12. Homework • Week 6 Worksheet, due Monday, September 23rd • Absolutely, NO late homework. • Go to msgiwa1.weebly.com to complete a survey • There will be a survey hidden on the website every week. • Complete surveys each Friday by 9 PM for a homework grade!

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