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Matrix Equalities & Variables
Matrices can be equal if certain conditions are satisfied. Therefore, we can set up equations and solve for variables with two equal matrices. (Note: this is different from a Matrix Equationin which an entire matrix acts as a variable.)
This Page: Variables & Matrices Other Pages: Introduction to Matrices | Matrix Equations | Real World Matrices Equal of Matrices Two matrices are equal if and only if these matrices have the same dimensions and equal corresponding elements.
Which matrices below are equal?
Which matrices below are equal?
Answer
Matrices #4 and #5 are equal. They have the same dimensions and equal corresponding entries. 
Which matrices below are equal?
Answer
Matrices #8 and #9 are equal. They have the same dimensions and equal corresponding entries. 
Which matrices below are equal?
Answer Matrix #10 and #11 are equal. Matrix #12 is ruled out because it does not have the same dimensions as the other two. It only has two columns. 
Solving for Variables in Matrices
If we know that two matrices are equal, we can find the value of variables in matrices. Since equal matrices have equal corresponding entries, we can set an unknown entry in one matrix equal to its corresponding partner in the other matrix.
To find the value of the variable y in the left hand matrix, we just set it equal to its corresponding entry in the right hand matrix.
y = 33 
Solving for variables in equal matrices will not always be as easy as matching a variable with a corresponding number. Here's a slightly more challenging problem: What is the value of y?
Answer
3y = 33 (set corresponding entries equal)
3y ÷3 =33÷3  y=11
This Page: Variables & Matrices Other Pages: Introduction to Matrices | Matrix Equations | Real World Matrices Top
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