How to Solve Matrix Equations

How to Solve Matrix Equations

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What is a Matrix Equation?

A matrix equation has the form AX = B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants on the right side of the equations in a system.

Solving Matrix Equation?

Let's figure out what X is in the equation AX = B. We did this by multiplying each side of the equation by (A1). (the inverse of A)

AX = B  A1 (AX) = A1 B

We know that A1A equals I, where I is the same-order identity matrix as A. So,

IX = A1 B

Also we know that: IX = X. So,

X = A1 B

The answer to the matrix equation is found here. This is also called the "inverse matrix equation," and the way to solve a set of equations by using the above formula is called the "inverse matrix method." So, here are the steps to use matrices to solve a set of equations:

  • Put the system into the form of the matrix equation AX = B.
  • Find the Inverse of A.
  • To get the answer, multiply it by the constant matrix B. i.e., X = A1B.

Free printable Worksheets

Exercises for Solving Matrix Equations

1) Find the answer: X + [25 73] = [42 49]

2) Find the answer: X  [113 58] = [1321 76]

3) Find the answer: 2Y + [923 157] = [827 133]

4) Find the answer: 2Y  [1521 1917] = [916 127]

5) Find the answer: 2X + [711 77] = [1529 1711]

6) Find the answer: 2X + [19208] = [253112]

7) Find the answer: X×[24 13] = [31 23]

8) Find the answer: X×[51 23] = [86 912]

9) Find the answer: 3X = [183369]

10) Find the answer: 7 Y = [704256]

 

1) Find the answer: X + [25 73] = [42 49]

X = [42 49]  [25 73] = [63 312]

2) Find the answer: X  [113 58] = [1321 76]

X = [113 58] + [1321 76] = [2424 1214]

3) Find the answer: 2Y + [923 157] = [827 133]

2Y = [827 133]  [923 157] = [174 2810]  Y = [8.52 145]

4) Find the answer: 2Y  [1521 1917] = [916 127]

2Y = [1521 1917] + [916 127] = [637 710]  Y = [318.5 3.55]

5) Find the answer: 2X + [711 77] = [1529 1711]

2X = [1529 1711]  [711 77] = [2240 244]  X = [1120 122]

6) Find the answer: 2X + [19208] = [253112]

2X = [253112]  [19208] = [61120]  X = [35.510]

7) Find the answer: X×[24 13] = [31 23]

X×[24 13] = [31 23]  X = [31 23]×[24 13]1  = [31 23]×[31025 11015]= [171032 11012]

8) Find the answer: X×[51 23] = [86 912]

X×[51 23] = [86 912]  X = [86 912]×[51 23]1  = [86 912]×[317117 217517]= [33173017 29174817]

9) Find the answer: 3X = [183369]

3X = [183369]  X = [61123]

10) Find the answer: 7 Y = [704256]

7 Y = [704256]  Y = [1068]

Matrix Equations Practice Quiz