Class 12 Matrices · Long Answer3 Marksmatrix_equality

Class 12 Maths · Matrices · Long Answer #64

Let A=\(\begin{bmatrix}2 & -1\\3 & 4\end{bmatrix}\), B=\(\begin{bmatrix}5 & 2\\7 & 4\end{bmatrix}\) and C=\(\begin{bmatrix}2 & 5\\3 & 8\end{bmatrix}\). Find D such that CD−AB=O.

✅ Step-by-Step Solution

Final Answer: \(\begin{bmatrix}-191 & -110\\77 & 44\end{bmatrix}\)

Compute AB=[[3,0],[43,22]]. The equation becomes CD=AB.
Writing D=[[a,b],[c,d]] gives 2a+5c=3, 3a+8c=43, 2b+5d=0 and 3b+8d=22.
Elimination gives c=77,a=−191 from the first two equations and d=44,b=−110 from the last two. Substitution gives CD=[[3,0],[43,22]].
Therefore D=\(\begin{bmatrix}-191 & -110\\77 & 44\end{bmatrix}\).

📋 CBSE Stepwise Marking Scheme

[0.5 marks] Compute AB=[[3,0],[43,22]]. The equation becomes CD=AB.
[1 mark] Writing D=[[a,b],[c,d]] gives 2a+5c=3, 3a+8c=43, 2b+5d=0 and 3b+8d=22.
[1 mark] Elimination gives c=77,a=−191 from the first two equations and d=44,b=−110 from the last two. Substitution gives CD=[[3,0],[43,22]].
[0.5 marks] Therefore D=\(\begin{bmatrix}-191 & -110\\77 & 44\end{bmatrix}\).

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Class 12 Maths · Matrices · Long Answer #64

✅ Step-by-Step Solution

📋 CBSE Stepwise Marking Scheme

Master Chapter 3: Matrices

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