Matrices
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
If $A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix}$ and $k A = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}$, then values of $k, a, b$ are:
(a) $k = -6, a = -4, b = -9$
(b) $k = 6, a = 4, b = 9$
(c) $k = -6, a = 4, b = 9$
(d) $k = 6, a = -4, b = -9$
Step-by-Step Solution
Equating entries: -4k = 24 => k = -6. 2k = 3a => -12 = 3a => a = -4. 3k = 2b => -18 = 2b => b = -9. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Selecting $k = -6, a = -4, b = -9$: 1.0 Mark
Correct Answer: $k = -6, a = -4, b = -9$
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