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How to solve a system of equations with a matrix on a TI-84 Plus CE, TI-84 Plus or TI-83 Plus

By E-Code · updated

Press 2nd MATRIX (above x⁻¹), ▶ twice to EDIT, ENTER, and type the size and each equation's numbers into [A] as a row. Back home, MATRIX ▶ MATH, ALPHA B for rref(, MATRIX 1 for [A], ) and ENTER: the last column is the answer.

Step by step

  1. Open MATRIX. 2nd X⁻¹ Press 2nd, then x⁻¹. MATRIX (above x⁻¹) has three tabs: NAMES MATH EDIT.
  2. Go to EDIT. ▶ ▶ Press ▶ twice to reach EDIT.
  3. Edit matrix [A]. ENTER Press ENTER to edit [A]. First it asks for its size: rows × columns.
  4. Make it 2 × 3. 2 ENTER 3 ENTER To solve x + y = 5 and x − y = 1, you need 2 rows (one per equation) and 3 columns: x, y, and the answer. Type 2 ENTER 3 ENTER.
  5. Type the numbers. 1 ENTER 1 ENTER 5 ENTER 1 ENTER (-) 1 ENTER 1 ENTER Type each number and ENTER, row by row: 1, 1, 5 for x + y = 5, then 1, (−)1, 1 for x − y = 1.
  6. Go back home. 2nd MODE Press 2nd, then MODE (QUIT). [A] is kept.
  7. MATRIX again. 2nd X⁻¹ Press 2nd, then x⁻¹.
  8. The MATH tab. ▶ Press ▶ once for MATH, the matrix tools.
  9. Pick rref(. ALPHA APPS Press ALPHA, then APPS. B (above APPS) picks B:rref(, reduced row-echelon form.
  10. Open the matrix names. 2nd X⁻¹ Press 2nd, then x⁻¹. The NAMES tab lists the matrices.
  11. Pick [A]. 1 Press 1 for [A].
  12. Solve it. ) ENTER Press ) and ENTER.
  13. Read the last column. [[1 0 3][0 1 2]] reads as 1x = 3 and 1y = 2: x = 3, y = 2. The same works for 3 equations in a 3 × 4 matrix.

What the screen shows

[[1 0 3][0 1 2]] reads as 1x = 3 and 1y = 2: x = 3, y = 2. The same works for 3 equations in a 3 × 4 matrix.

Look for [0 1 2]] on the screen.

Try it with the keys lit up

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