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If  then find the value of (-A2 + 6 A) ?

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Option 2 :
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Detailed Solution

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Concept:

Scalar Multiplication:

If any matrix is multiplied by a scalar k ∈ R, then each element of the matrix is multiplied by k i.e If A = [aij]m × n then k × A = A = [k × aij]m × n

Multiplication of Matrices:

If A and B are two matrices such that the no. of columns of A is equal to the no. of rows of B. If A = [aij] is a m × n matrix and B = [bij] be a n × p matrix, then the product AB is the resultant matrix of order m × p and is defined as:

Calculation:

Given: 

Here, we have to find the value of the expression: ( A2 + 6 A)

 and 

Hence, 

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Q1.Consider the following in respect of the matrices  \(\rm P=\begin{bmatrix}0&c&-b\\\ -c&0&a\\\ b&-a&0\end{bmatrix}\ and\ \rm Q=\begin{bmatrix}a^2&ab&ac\\\ ab&b^2&bc\\\ ac&bc&c^2\end{bmatrix}\) I. PQ is a null matrix.  II. QP is an identity matrix of order 3.  III. PQ = QP Which of the above is/are correct? 
Q2.Let X be a matrix of order 3 x 3, Y be a matrix of order 2 x 3 and Z be a matrix of order 3 × 2. Which of the following statements are correct? I. (ZY)X is defined and is a square matrix of order 3. II. Y(XZ) is defined and is a square matrix of order 2. III. X(YZ) is not defined. Select the answer using the code given below.
Q3.If \(A=\left[\begin{array}{cc} 1 & 3 \\ 0 & -1 \end{array}\right]\), then trace of 5A5 + 4A4 + 3A3 + 2A2 + A + I2 is :
Q4.Find the additive inverse of matrix A = \(\left[\begin{array}{cc}2 & 1 \\ −3 & 0\end{array}\right]\)
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Q6.On using elementary row operation R1 → R1 – 3R2 in the following matrix equation: \(\left[\begin{array}{ll}4 & 2 \\ 3 & 3\end{array}\right] = \left[\begin{array}{ll}1 & 2 \\ 0 & 3\end{array}\right]\left[\begin{array}{ll}2 & 0 \\ 1 & 1\end{array}\right]\), we have :
Q7.On using elementary column operations C2 → C2 – 2C1 in the following matrix equation \(\left[\begin{array}{cc}1 & −3 \\ 2 & 4\end{array}\right] = \left[\begin{array}{cc}1 & −1 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}3 & 1 \\ 2 & 4\end{array}\right]\), we have :
Q8.For any two matrices A and B, we have
Q9.If A = \(\left[\begin{array}{ccc}2 & −1 & 3 \\ −4 & 5 & 1\end{array}\right]\) and B = \(\left[\begin{array}{cc}2 & 3 \\ 4 & −2 \\ 1 & 5\end{array}\right]\), then
Q10.If A and B are square matrices of the same order, then (A + B) (A – B) is equal to

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Q1.What is A-1 equal to?  
Q2.What is A(adj A) equal to?  
Q3.Consider the following in respect of the matrices  \(\rm P=\begin{bmatrix}0&c&-b\\\ -c&0&a\\\ b&-a&0\end{bmatrix}\ and\ \rm Q=\begin{bmatrix}a^2&ab&ac\\\ ab&b^2&bc\\\ ac&bc&c^2\end{bmatrix}\) I. PQ is a null matrix.  II. QP is an identity matrix of order 3.  III. PQ = QP Which of the above is/are correct? 
Q4.Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct? 
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Q6.If \(A=\left[\begin{array}{cc} 1 & 3 \\ 0 & -1 \end{array}\right]\), then trace of 5A5 + 4A4 + 3A3 + 2A2 + A + I2 is :
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Q8.Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A2B2 − B2A2)X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has:
Q9.Let α ∈ (0, α) and \(A = \begin{bmatrix} 1 & 2 & \alpha \\\ 1 & 0 & 1 \\\ 0 & 1 & 2 \end{bmatrix}\). If det(adj(2A - AT). adj(A - 2AT)) = 28, then (det(A))2 is equal to: 
Q10.For a 3 × 3 matrix A = [aij], whose element aij is given by aij = \(\rm \sqrt{i^2+3j}\) then what is element a31?
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