Mathematics Grade 5 15 min

Solve a system of equations using augmented matrices

Solve a system of equations using augmented matrices

What you'll learn

  • Identify the coefficient matrix, variable matrix, and constant matrix from a given system of linear equations in two or three variables.
  • Apply elementary row operations (swapping rows, multiplying a row by a non-zero constant, adding a multiple of one row to another) to transform an augmented matrix into row-echelon form.
  • Solve a system of two or three linear equations by transforming the corresponding augmented matrix into reduced row-echelon form and interpreting the solution.
  • Explain the relationship between the row-echelon form of an augmented matrix and the existence and uniqueness of solutions to the corresponding system of linear equations (i.e., no solution, unique solution, or infinitely many solutions).

Tutorial Preview

1

A cupcake and a cookie cost $4. Two cupcakes and a cookie cost $6. How much is one cupcake?

2

We know a cupcake costs $2. If a cupcake and a cookie cost $4, how much is one cookie?

3

A cupcake costs $2 and a cookie costs $2. How much do 3 cupcakes and 2 cookies cost?

Sample Practice Questions

Easy
One apple and one banana cost $3. Two apples and one banana cost $5. How much is one apple?
0.$1
1.$2
2.$3
3.$4
Easy
A pen and an eraser cost 50¢. Two pens and an eraser cost 80¢. How much is one pen?
0.20¢
1.30¢
2.40¢
3.50¢
Easy
A taco costs $3. A taco and a soda cost $5. How much is the soda?
0.$1
1.$2
2.$3
3.$8

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Frequently asked questions

What grade level is "Solve a system of equations using augmented matrices"?

Solve a system of equations using augmented matrices is a Grade 5 Mathematics lesson on ExcelOS.

What will I learn in Solve a system of equations using augmented matrices?

You'll be able to: Identify the coefficient matrix, variable matrix, and constant matrix from a given system of linear equations in two or three variables; Apply elementary row operations (swapping rows, multiplying a row by a non-zero constant….

Is "Solve a system of equations using augmented matrices" free to practice?

Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.

How many practice questions are included with Solve a system of equations using augmented matrices?

This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.

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