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Evaluate : if possible (i) [3,2] [{:(,...

Evaluate : if possible
(i) `[3,2] [{:(,2),(,0):}]` (ii) `[1 , -2] [{:(,-2,3),(,-1,4):}]`
(iii) `[{:(,6,4),(,3,-1):}] [{:(,-1),(,3):}]` (iv) `[{:(,6,4),(,3,-1):}] [{:(,-1),(,3):}]`

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Let's evaluate each part step by step. ### Part (i): Evaluate `[3, 2]` and `[{(2),(0)}]` 1. Identify the dimensions of the matrices: - The first matrix `[3, 2]` is a 1x2 matrix. - The second matrix `[{(2),(0)}]` is a 2x1 matrix. 2. Check if multiplication is possible: - The number of columns in the first matrix (2) matches the number of rows in the second matrix (2). Therefore, multiplication is possible. 3. Perform the multiplication: \[ [3, 2] \cdot \begin{bmatrix} 2 \\ 0 \end{bmatrix} = (3 \cdot 2) + (2 \cdot 0) = 6 + 0 = 6 \] ### Part (ii): Evaluate `[1, -2]` and `[{(-2, 3), (-1, 4)}]` 1. Identify the dimensions of the matrices: - The first matrix `[1, -2]` is a 1x2 matrix. - The second matrix `[{(-2, 3), (-1, 4)}]` is a 2x2 matrix. 2. Check if multiplication is possible: - The number of columns in the first matrix (2) matches the number of rows in the second matrix (2). Therefore, multiplication is possible. 3. Perform the multiplication: \[ [1, -2] \cdot \begin{bmatrix} -2 & 3 \\ -1 & 4 \end{bmatrix} = (1 \cdot -2 + -2 \cdot -1, 1 \cdot 3 + -2 \cdot 4) \] \[ = (-2 + 2, 3 - 8) = (0, -5) \] ### Part (iii): Evaluate `[{(6, 4), (3, -1)}]` and `[{(-1), (3)}]` 1. Identify the dimensions of the matrices: - The first matrix `[{(6, 4), (3, -1)}]` is a 2x2 matrix. - The second matrix `[{(-1), (3)}]` is a 2x1 matrix. 2. Check if multiplication is possible: - The number of columns in the first matrix (2) matches the number of rows in the second matrix (2). Therefore, multiplication is possible. 3. Perform the multiplication: \[ \begin{bmatrix} 6 & 4 \\ 3 & -1 \end{bmatrix} \cdot \begin{bmatrix} -1 \\ 3 \end{bmatrix} = (6 \cdot -1 + 4 \cdot 3, 3 \cdot -1 + -1 \cdot 3) \] \[ = (-6 + 12, -3 - 3) = (6, -6) \] ### Part (iv): Evaluate `[{(6, 4), (3, -1)}]` and `[{(-1), (3)}]` This part is identical to part (iii), so the evaluation will yield the same result. 1. The result is: \[ (6, -6) \] ### Summary of Results: - Part (i): 6 - Part (ii): (0, -5) - Part (iii): (6, -6) - Part (iv): (6, -6)
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Wherever possible write each of the following as a single matrix. (i) [{:(,1,2),(,3,4):}]+[{:(,-1,-2),(,1,-7):}] (ii) [{:(,2,3,4),(,5,6,7):}]-[{:(,0,2,3),(,6,-1,0):}] (iii) [{:(,0,1,2),(,4,6,7):}]+[{:(,3,4),(,6,8):}]

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ICSE-MATRICES-Exercise 9C
  1. Evaluate : if possible (i) [3,2] [{:(,2),(,0):}] (ii) [1 , -2] [{:(,...

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  2. If A=[{:(,0,2),(,5,-2):}], B=[{:(,1,-1),(,3,2):}] and is a unit matri...

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  3. If A=[{:(,3,x),(,0,1):}] and B=[{:(,9,16),(,0,-y):}] find x and y when...

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  4. Find x and y, if : (i) [{:(,4,3x),(,x,-2):}] [{:(,5),(,1):}]=[{:(,y,...

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  5. If A=[{:(,1,3),(,2,4):}], B=[{:(,1,2),(,4,3):}] and C=[{:(,4,3),(,1,2)...

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  6. Given A=[{:(,0,4,6),(,3,0,-1):}] and B=[{:(,0,1),(,-1,2),(,-5,-6):}], ...

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  7. Let A=[{:(,2,1),(,0,-2):}], B=[{:(,4,1),(,-3,-2):}] and C=[{:(,-3,2),(...

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  8. If M=[{:(,1,2),(,2,1):}] and I is a unit matrix of the same order as t...

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  9. If A=[{:(,a,0),(,0,2):}], B=[{:(,0,-b),(,1,0):}], M=[{:(,1,-1),(,1,1):...

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  10. Given A=[{:(,4,1),(,2,3):}] and B=[{:(,1,0),(,-2,01):}], Find (i) A-...

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  11. If A=[{:(,1,4),(,1,-3):}] and B=[{:(,1,2),(,-1,-1):}], find: (A+B)...

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  12. Find the matrix A, if B=[{:(,2,1),(,0,1):}] and B^2=B+1/2A.

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  13. If A=[{:(,-1,1),(,a,b):}] and A^2=I, find a and b.

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  14. If A=[{:(,2,1),(,0,0):}], B=[{:(,2,3),(,4,1):}] and C=[{:(,1,4),(,0,2)...

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  15. If A=[{:(,1,4),(,2,1):}], B=[{:(,-3,2),(,4,0):}] and C=[{:(,1,0),(,0,2...

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  16. Solve for x and y (i) [{:(,2,5),(,5,2):}] [{:(,x),(,y):}]=[{:(,-7),(...

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  17. In each case given below, find : the order of matrix M, (i) M ...

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  18. If A=[{:(,2,x),(,0,1):}] and B=[{:(,4,36),(,0,1):}], find the value of...

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  19. If A=[{:(,3,7),(,2,4):}], B=[{:(,0,2),(,5,3):}] and C=[{:(,1,-5),(,-4,...

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  20. If A and B are any two 2 xx 2 matrices such that AB=BA=B and B is not ...

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