matrix equation calculator 2x2

This result gives us a method for solving simultaneous equations All we need do is write them in matrix form, calculate the inverse of the matrix of coefficients, 

solving two linear equations in two variables, we use matrices and matrix Solving a System Using a Graphing Calculator Solve to two deci- x1 + 2x2 = -3

Check your answers All 2x2 systems must be done by hand Systems 3x3 and larger may be solved with a calculator, However, show the matrix equation for all  

Solve for X 2x2 by hand, 3x3 with calculator 2 -1 0 1–5 5) 1 4 2 X = calculator However, show the matrix equation for all systems 3x - 7y=7 6) 17x + 3y = 3

Solve systems of two linear equations in two variables by using graphing calculators Use these matrices and a graphing calculator to answer Items 2-4 12 4 hy] =22] 2x2 21 is A"? A=123 coefficient matrix A constant matrix B AX if it is

I can use matrices to solve systems of linear equations • I can use 3 Now use your calculator to verify wliad you found in #2 Verified (2x2 + 3x2 – 2x3 = 2 a

Items 1 - 11 · for the linear equation system x1 + 2x2 + x3 = 3 2x1 + 5x2 + 2x3 = 8 −3x1 − 4x2 − 2x3 = −4 (6) 1 2 Row-echelon form of a matrix 1 2 1

Given a system of linear equations in two unknowns { −2x + 4y = 2 a1,1x1 + a1,2x2 + ··· + a1,nxn = b1 a2,1x1 + a2,2x2 + ··· + We then calculate A−1 and multiply the equation AX = B by the matrix A−1 to get and equation of the form X  

2x2 2*1 product = 2X1 Writing a Matrix Equation: Write the system of linear Because we can't calculate a 3x3 inverse by hand, we must use the calculator

Consider a system of two simultaneous linear equations: Multiply Equation the matrix equation calculate the inverse matrix transformations To apply a rotation and a reflection to 2D vectors, two 2x2 matrices can be used to transform the