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If P and Q are two different matrices of order 3 x 4 and 4 x 3 respectively, then the order of matrix QP is
The order of a product of two matrices depends upon the order of the given matrices. Given: Matrix P has an order of 3 × 4 Matrix Q has an order of 4 × 3 For the matrix multiplication QP to be defined, the number of columns of Q must equal the number of rows of P. Since Q is 4 × 3 and P is 3 × 4, thRead more
The order of a product of two matrices depends upon the order of the given matrices. Given: Matrix P has an order of 3 × 4 Matrix Q has an order of 4 × 3 For the matrix multiplication QP to be defined, the number of columns of Q must equal the number of rows of P.
Since Q is 4 × 3 and P is 3 × 4, the multiplication QP is not possible
Since the question asks for the order of QP, but the multiplication is undefined, none of the given options are correct.
If the question meant PQ instead of QP, then:
– The order of PQ would be 3 × 3 since P is 3 × 4 and Q is 4 × 3.
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Suppose P and Q are two different matrices of order 3 x n and n x p, then the order of the matrix P x Q is
P is a 3 × n order matrix Q is an n × p order matrix For multiplication of matrices P × Q to be possible, the number of columns of P and the number of rows of Q must be equal. P has n columns. Q has n rows. Thus, multiplication is possible. The order of the resulting matrix will be determined by theRead more
P is a 3 × n order matrix
Q is an n × p order matrix
For multiplication of matrices P × Q to be possible, the number of columns of P and the number of rows of Q must be equal.
P has n columns.
Q has n rows.
Thus, multiplication is possible.
The order of the resulting matrix will be determined by the number of rows of P and the number of columns of Q, so the order of P × Q will be 3 × p.
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If A is a square matrix and A² = A, then (I + A)² – 3A is equal to:
Given that A is a square matrix and A² = A, we must reduce (I + A)² - 3A. Step 1: Expand (I + A)² (I + A)² = I² + 2IA + A² Given that I² = I and A² = A, we get: (I + A)² = I + 2A + A (I + A)² = I + 3A Step 2: Subtract 3A Substitute this back into the expression: (I + A)² - 3A = (I + 3A) - 3A (I + A)Read more
Given that A is a square matrix and A² = A, we must reduce (I + A)² – 3A.
Step 1: Expand (I + A)²
(I + A)² = I² + 2IA + A²
Given that I² = I and A² = A, we get:
(I + A)² = I + 2A + A
(I + A)² = I + 3A
Step 2: Subtract 3A
Substitute this back into the expression:
(I + A)² – 3A = (I + 3A) – 3A
(I + A)² – 3A = I
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Given that matrices A and B are of order 3 x n and m x 5 respectively, then the order of matrix C = 5A + 3B is:
Matrix A has order 3 × n, and B has order m × 5; find the order of matrix C = 5A + 3B Step 1: Rules governing addition of matrices Addition is defined only when both matrices are the same order, and the same with our scenario of A versus B. Matrix A has order 3 × n and matrix B has order m × 5. ForRead more
Matrix A has order 3 × n, and B has order m × 5; find the order of matrix C = 5A + 3B
Step 1: Rules governing addition of matrices
Addition is defined only when both matrices are the same order, and the same with our scenario of A versus B.
Matrix A has order 3 × n and matrix B has order m × 5.
For the addition 5A + 3B to be possible, we must have n = m, meaning both matrices must have the same number of columns.
Step 2: Order of matrix C
Once the condition n = m is met, then the matrix C that results from it will be of the same order as that of A and B, which is 3 × 5.
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If order of matrix A is 2 x 3 of matrix B is 3 x 2, and of matrix C is 3 x 3, then which one of the following is not defined?
- Matrix A has order 2 × 3 and matrix B has order 3 × 2. - The transpose of matrix B, B', has order 2 × 3. - For the sum A + B', both matrices have order 2 × 3, so the addition is possible. - However, matrix C has order 3 × 3, and for matrix multiplication to be defined, the number of columns in matRead more
– Matrix A has order 2 × 3 and matrix B has order 3 × 2.
– The transpose of matrix B, B’, has order 2 × 3.
– For the sum A + B’, both matrices have order 2 × 3, so the addition is possible.
– However, matrix C has order 3 × 3, and for matrix multiplication to be defined, the number of columns in matrix C (3) must match the number of rows in A + B’ (2).
– Since 3 ≠ 2, multiplying matrix C by A + B’ is not defined.
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