A, B and C are three square matrices each of order 3; the order of matrix CA + B² is :
3 × 1
3 × 3
1 × 3
2 × 3
Matrices
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Question

A, B and C are three square matrices each of order 3; the order of matrix CA + B2 is : 1. 3 × 1 2. 3 × 3 3. 1 × 3 4. 2 × 3

KnowledgeBoat · Accepted Answer

Let resultant matrix of CA be R. C3 × 3 × A3 × 3 = Rm × n We know that, For matrix multiplication : No. of columns in C must be equal to the number of rows in A. Resultant matrix order = No. of rows in C × No. of columns in A. ∴ m = 3 and n = 3. ∴ Order of matrix R will be 3 × 3. Let resultant matrix of B2 be S. B3 × 3 × B3 × 3 = Sg × h Resultant matrix order = No. of rows in B × No. of columns in B. ∴ g = 3 and h = 3. ∴ Order of matrix S will be 3 × 3. ⇒ CA + B2 ⇒ R + S Addition of matrix possible between matrix of same order and same is the order of resultant matrix. Hence, resultant matrix's order = 3 × 3. Hence, Option 2 is the correct option.

Mathematics

A, B and C are three square matrices each of order 3; the order of matrix CA + B² is :
3 × 1
3 × 3
1 × 3
2 × 3

Matrices

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Mathematics

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