Question:
If \( \begin{pmatrix} 3x-y & x+3y \\ 2x-z & 2y+z \end{pmatrix} = \begin{pmatrix} 7 & 9 \\ 5 & 5 \end{pmatrix} \), then \( x+y+z \) equals
If \( \begin{pmatrix} 3x-y & x+3y \\ 2x-z & 2y+z \end{pmatrix} = \begin{pmatrix} 7 & 9 \\ 5 & 5 \end{pmatrix} \), then \( x+y+z \) equals
Show Hint
Matrix equality gives system of equations.
Updated On: Apr 30, 2026
- \(3\)
- \(6\)
- \(9\)
- \(12\)
- \(11\)
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The Correct Option is B
Solution and Explanation
Concept:
Equal matrices ⇒ corresponding elements equal.
Step 1: Equate entries. \[ 3x - y = 7 ...(1) \] \[ x + 3y = 9 ...(2) \] \[ 2x - z = 5 ...(3) \] \[ 2y + z = 5 ...(4) \]
Step 2: Solve (1) and (2). From (2): \[ x = 9 - 3y \] Substitute into (1): \[ 3(9-3y) - y = 7 \] \[ 27 - 9y - y = 7 \] \[ 27 -10y = 7 \] \[ 10y = 20 \Rightarrow y=2 \] Then: \[ x = 9 - 6 = 3 \]
Step 3: Find \(z\). From (4): \[ 2(2)+z = 5 \] \[ z = 1 \]
Step 4: Final sum. \[ x+y+z = 3+2+1 = 6 \]
Step 1: Equate entries. \[ 3x - y = 7 ...(1) \] \[ x + 3y = 9 ...(2) \] \[ 2x - z = 5 ...(3) \] \[ 2y + z = 5 ...(4) \]
Step 2: Solve (1) and (2). From (2): \[ x = 9 - 3y \] Substitute into (1): \[ 3(9-3y) - y = 7 \] \[ 27 - 9y - y = 7 \] \[ 27 -10y = 7 \] \[ 10y = 20 \Rightarrow y=2 \] Then: \[ x = 9 - 6 = 3 \]
Step 3: Find \(z\). From (4): \[ 2(2)+z = 5 \] \[ z = 1 \]
Step 4: Final sum. \[ x+y+z = 3+2+1 = 6 \]
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