Question:
If \(
\begin{pmatrix}
-1 & 2
3 & -4
-5 & 6
\end{pmatrix}
\begin{pmatrix}
7
8
\end{pmatrix}
=
\begin{pmatrix}
\alpha
\beta
13
\end{pmatrix}
\), then the value of \( \alpha + \beta \) is equal to
If \(
\begin{pmatrix}
-1 & 2
3 & -4
-5 & 6
\end{pmatrix}
\begin{pmatrix}
7
8
\end{pmatrix}
=
\begin{pmatrix}
\alpha
\beta
13
\end{pmatrix}
\), then the value of \( \alpha + \beta \) is equal to
Show Hint
Always multiply row-wise for matrices and verify with given result if possible.
Updated On: Apr 21, 2026
- \(-18 \)
- \(18 \)
- \(21 \)
- \(-21 \)
- \(-2 \)
Show Solution
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The Correct Option is
Solution and Explanation
Concept:
Matrix multiplication: row × column.
Step 1: Compute \( \alpha \).
\[ \alpha = (-1)(7) + (2)(8) = -7 + 16 = 9 \]
Step 2: Compute \( \beta \).
\[ \beta = (3)(7) + (-4)(8) = 21 - 32 = -11 \]
Step 3: Verify third value.
\[ (-5)(7) + (6)(8) = -35 + 48 = 13 \quad \checkmark \]
Step 4: Find sum.
\[ \alpha + \beta = 9 + (-11) = -2 \]
Step 1: Compute \( \alpha \).
\[ \alpha = (-1)(7) + (2)(8) = -7 + 16 = 9 \]
Step 2: Compute \( \beta \).
\[ \beta = (3)(7) + (-4)(8) = 21 - 32 = -11 \]
Step 3: Verify third value.
\[ (-5)(7) + (6)(8) = -35 + 48 = 13 \quad \checkmark \]
Step 4: Find sum.
\[ \alpha + \beta = 9 + (-11) = -2 \]
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