7. (12%) Suppose matrix . Find a matrix B such that B ● B = A. 

(A)(3%) Compute det(adj(A)).

(B)(3%) Compute

(C)(4%) Prove that det= adj(adj(A)).

9. (12%) . Please compute the QR decomposition of A, where Q is an  orthonormal matrix and R is an upper-triangular matrix.

10.(8%) Find a matrix representation A for the reflection of the plane in the line y = mx. (Hint : Assume that b1 is a Vector which lies along the line y = mx, and b2 is a vector which is orthogonal to b1.) 

2.1 (10%) What is the CPI if this single-core processor only has one level of cache?

2.2 (20%) To speed up the process, we increase the CPU cores from 1-core CPU to 2-core CPU and retain other design settings. We assume 60% of instructions must be executed sequentially. Please estimate the speedup ratio by using the new architecture.

3. (20%) Assume a GPU architecture that contains 10 SIMD processors. Each SIMD instruction has a width of 32 and each SIMD process ssor contains 8 lanes for single-precision arithmetic and load/store instructions, meaning that each non-diverged SIMD instruction can produce 32 results every 4 cycles. Assume a kernel that has divergent branches that cause on average 80% of threads to be active. Assume that 70% of all SIMD instructions executed are single-precision arithmetic and 20% are load/store. Since not all memory latencies are covered, assume an average SIMD instruction issue rate of 0.85. Assume that the GPU has a clock speed of 1.5 GHz. Please compute the throughput, in GFLOP/sec, for this kernel on this GPU. 

4.1 (10%) Please determine the number of bits required in the page table, TLB in the L1 cache, and TLB in the L2 cache.

a. (5%) L1 cache is implemented by using 2-way associative mapping strategy.

114年 - [無官方正解]114 臺灣綜合大學系統_學士班轉學生考試試題:線性代數#137898

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